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mode 100644 _images/tutorial_19_0.png create mode 100644 _images/tutorial_5_1.png create mode 100644 _modules/pina/model/base_no.html create mode 100644 _rst/models/base_no.html create mode 100644 _rst/models/fourier_kernel.html create mode 100644 _rst/tutorials/tutorial8/tutorial.html create mode 100644 _sources/_rst/models/base_no.rst.txt create mode 100644 _sources/_rst/models/fourier_kernel.rst.txt create mode 100644 _sources/_rst/tutorials/tutorial8/tutorial.rst.txt diff --git a/.buildinfo b/.buildinfo index 5fee18e6..b73df63f 100644 --- a/.buildinfo +++ b/.buildinfo @@ -1,4 +1,4 @@ # Sphinx build info version 1 # This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done. -config: a765572ea3a7b0e12f8c5177dc95c950 +config: e773860857a5b1a8ff889f437af7e263 tags: 645f666f9bcd5a90fca523b33c5a78b7 diff --git a/_LICENSE.html b/_LICENSE.html index af5276e7..7eef76bb 100644 --- a/_LICENSE.html +++ b/_LICENSE.html @@ -1,11 +1,13 @@ - + - License — PINA 0.1 documentation + License — PINA 0.1.0.post2403 documentation - + + + @@ -37,7 +39,7 @@
- 0.1 + 0.1.0.post2403
@@ -120,8 +122,8 @@

License -

© Copyright Copyright 2021-2023, PINA Contributors. - Last updated on Nov 17, 2023. +

© Copyright Copyright 2021-2024, PINA Contributors. + Last updated on Mar 01, 2024.

diff --git a/_cite.html b/_cite.html index 1c970b41..bcdcd7bb 100644 --- a/_cite.html +++ b/_cite.html @@ -1,11 +1,13 @@ - + - Cite PINA — PINA 0.1 documentation + Cite PINA — PINA 0.1.0.post2403 documentation - + + + @@ -36,7 +38,7 @@
- 0.1 + 0.1.0.post2403
@@ -116,8 +118,8 @@

Cite PINA -

© Copyright Copyright 2021-2023, PINA Contributors. - Last updated on Nov 17, 2023. +

© Copyright Copyright 2021-2024, PINA Contributors. + Last updated on Mar 01, 2024.

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- 0.1 + 0.1.0.post2403
@@ -105,6 +107,7 @@

All modules for which code is available

  • pina.geometry.union_domain
  • pina.label_tensor
  • pina.loss
    • +
  • pina.model.base_no
  • pina.model.deeponet
  • pina.model.feed_forward
  • pina.model.fno
    • @@ -134,8 +137,8 @@

    All modules for which code is available

    -

    © Copyright Copyright 2021-2023, PINA Contributors. - Last updated on Nov 17, 2023. +

    © Copyright Copyright 2021-2024, PINA Contributors. + Last updated on Mar 01, 2024.

    diff --git a/_modules/pina/callbacks/adaptive_refinment_callbacks.html b/_modules/pina/callbacks/adaptive_refinment_callbacks.html index 454131ff..8df26ef7 100644 --- a/_modules/pina/callbacks/adaptive_refinment_callbacks.html +++ b/_modules/pina/callbacks/adaptive_refinment_callbacks.html @@ -1,11 +1,13 @@ - + - pina.callbacks.adaptive_refinment_callbacks — PINA 0.1 documentation + pina.callbacks.adaptive_refinment_callbacks — PINA 0.1.0.post2403 documentation - + + + @@ -35,7 +37,7 @@
    - 0.1 + 0.1.0.post2403
    @@ -87,7 +89,7 @@

    Source code for pina.callbacks.adaptive_refinment_callbacks

    -'''PINA Callbacks Implementations'''
+"""PINA Callbacks Implementations"""
 
 # from lightning.pytorch.callbacks import Callback
 from pytorch_lightning.callbacks import Callback
@@ -97,18 +99,17 @@ 
    Source code for pina.callbacks.adaptive_refinment_callbacks
    [docs]class R3Refinement(Callback):
 
-
     def __init__(self, sample_every):
         """
         PINA Implementation of an R3 Refinement Callback.
 
         This callback implements the R3 (Retain-Resample-Release) routine for sampling new points based on adaptive search.
-        The algorithm incrementally accumulates collocation points in regions of high PDE residuals, and releases those 
+        The algorithm incrementally accumulates collocation points in regions of high PDE residuals, and releases those
         with low residuals. Points are sampled uniformly in all regions where sampling is needed.
 
         .. seealso::
 
-            Original Reference: Daw, Arka, et al. *Mitigating Propagation Failures in Physics-informed Neural Networks 
+            Original Reference: Daw, Arka, et al. *Mitigating Propagation Failures in Physics-informed Neural Networks
             using Retain-Resample-Release (R3) Sampling. (2023)*.
             DOI: `10.48550/arXiv.2207.02338
             <https://doi.org/10.48550/arXiv.2207.02338>`_
@@ -168,7 +169,7 @@ 
    Source code for pina.callbacks.adaptive_refinment_callbacks
    # !!!!!! From now everything is performed on CPU !!!!!!
 
         # average loss
-        avg = (tot_loss.mean()).to('cpu')
+        avg = (tot_loss.mean()).to("cpu")
 
         # points to keep
         old_pts = {}
@@ -179,25 +180,29 @@ 
    Source code for pina.callbacks.adaptive_refinment_callbacks
    pts = pts.cpu().detach()
             residuals = res_loss[location].cpu()
             mask = (residuals > avg).flatten()
-            if any(mask): # if there are residuals greater than averge we append them
-                pts = pts[mask] # TODO masking remove labels
+            if any(
+                mask
+            ):  # if there are residuals greater than averge we append them
+                pts = pts[mask]  # TODO masking remove labels
                 pts.labels = labels
                 old_pts[location] = pts
                 tot_points += len(pts)
 
         # extract new points to sample uniformally for each location
         n_points = (self._tot_pop_numb - tot_points) // len(
-            self._sampling_locations)
+            self._sampling_locations
+        )
         remainder = (self._tot_pop_numb - tot_points) % len(
-            self._sampling_locations)
+            self._sampling_locations
+        )
         n_uniform_points = [n_points] * len(self._sampling_locations)
         n_uniform_points[-1] += remainder
 
         # sample new points
         for numb_pts, loc in zip(n_uniform_points, self._sampling_locations):
-            trainer._model.problem.discretise_domain(numb_pts,
-                                                     'random',
-                                                     locations=[loc])
+            trainer._model.problem.discretise_domain(
+                numb_pts, "random", locations=[loc]
+            )
         # adding previous population points
         trainer._model.problem.add_points(old_pts)
 
@@ -222,7 +227,7 @@ 
    Source code for pina.callbacks.adaptive_refinment_callbacks
    locations = []
         for condition_name in problem.conditions:
             condition = problem.conditions[condition_name]
-            if hasattr(condition, 'location'):
+            if hasattr(condition, "location"):
                 locations.append(condition_name)
         self._sampling_locations = locations
 
@@ -257,8 +262,8 @@ 
    Source code for pina.callbacks.adaptive_refinment_callbacks
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/callbacks/optimizer_callbacks.html b/_modules/pina/callbacks/optimizer_callbacks.html
index 882e319e..dd9fcc85 100644
--- a/_modules/pina/callbacks/optimizer_callbacks.html
+++ b/_modules/pina/callbacks/optimizer_callbacks.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.callbacks.optimizer_callbacks — PINA 0.1 documentation
+  pina.callbacks.optimizer_callbacks — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -87,7 +89,7 @@
            
    
              
   
    Source code for pina.callbacks.optimizer_callbacks
    -'''PINA Callbacks Implementations'''
+"""PINA Callbacks Implementations"""
 
 from pytorch_lightning.callbacks import Callback
 import torch
@@ -103,7 +105,7 @@ 
    Source code for pina.callbacks.optimizer_callbacks
            This callback allows for switching between different optimizers during training, enabling
         the exploration of multiple optimization strategies without the need to stop training.
 
-        :param new_optimizers: The model optimizers to switch to. Can be a single 
+        :param new_optimizers: The model optimizers to switch to. Can be a single
                             :class:`torch.optim.Optimizer` or a list of them for multiple model solvers.
         :type new_optimizers: torch.optim.Optimizer | list
         :param new_optimizers_kwargs: The keyword arguments for the new optimizers. Can be a single dictionary
@@ -112,7 +114,7 @@ 
    Source code for pina.callbacks.optimizer_callbacks
            :param epoch_switch: The epoch at which to switch to the new optimizer.
         :type epoch_switch: int
 
-        :raises ValueError: If `epoch_switch` is less than 1 or if there is a mismatch in the number of 
+        :raises ValueError: If `epoch_switch` is less than 1 or if there is a mismatch in the number of
                             optimizers and their corresponding keyword argument dictionaries.
 
         Example:
@@ -128,7 +130,7 @@ 
    Source code for pina.callbacks.optimizer_callbacks
    check_consistency(epoch_switch, int)
 
         if epoch_switch < 1:
-            raise ValueError('epoch_switch must be greater than one.')
+            raise ValueError("epoch_switch must be greater than one.")
 
         if not isinstance(new_optimizers, list):
             new_optimizers = [new_optimizers]
@@ -137,10 +139,12 @@ 
    Source code for pina.callbacks.optimizer_callbacks
    len_optimizer_kwargs = len(new_optimizers_kwargs)
 
         if len_optimizer_kwargs != len_optimizer:
-            raise ValueError('You must define one dictionary of keyword'
-                             ' arguments for each optimizers.'
-                             f' Got {len_optimizer} optimizers, and'
-                             f' {len_optimizer_kwargs} dicitionaries')
+            raise ValueError(
+                "You must define one dictionary of keyword"
+                " arguments for each optimizers."
+                f" Got {len_optimizer} optimizers, and"
+                f" {len_optimizer_kwargs} dicitionaries"
+            )
 
         # save new optimizers
         self._new_optimizers = new_optimizers
@@ -161,10 +165,13 @@ 
    Source code for pina.callbacks.optimizer_callbacks
    if trainer.current_epoch == self._epoch_switch:
             optims = []
             for idx, (optim, optim_kwargs) in enumerate(
-                    zip(self._new_optimizers, self._new_optimizers_kwargs)):
+                zip(self._new_optimizers, self._new_optimizers_kwargs)
+            ):
                 optims.append(
-                    optim(trainer._model.models[idx].parameters(),
-                          **optim_kwargs))
+                    optim(
+                        trainer._model.models[idx].parameters(), **optim_kwargs
+                    )
+                )
 
             trainer.optimizers = optims
    
 
    
@@ -176,8 +183,8 @@ 
    Source code for pina.callbacks.optimizer_callbacks
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/callbacks/processing_callbacks.html b/_modules/pina/callbacks/processing_callbacks.html
index 5351977e..826a16b6 100644
--- a/_modules/pina/callbacks/processing_callbacks.html
+++ b/_modules/pina/callbacks/processing_callbacks.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.callbacks.processing_callbacks — PINA 0.1 documentation
+  pina.callbacks.processing_callbacks — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -87,7 +89,7 @@
            
    
              
   
    Source code for pina.callbacks.processing_callbacks
    -'''PINA Callbacks Implementations'''
+"""PINA Callbacks Implementations"""
 
 from pytorch_lightning.callbacks import Callback
 import torch
@@ -95,7 +97,7 @@ 
    Source code for pina.callbacks.processing_callbacks
    [docs]class MetricTracker(Callback):
-    
+
     def __init__(self):
         """
         PINA Implementation of a Lightning Callback for Metric Tracking.
@@ -128,8 +130,9 @@ 
    Source code for pina.callbacks.processing_callbacks
            :return: None
         :rtype: None
         """
-        self._collection.append(copy.deepcopy(
-            trainer.logged_metrics))  # track them
    
+        self._collection.append(
+            copy.deepcopy(trainer.logged_metrics)
+        )  # track them
    
 
     @property
     def metrics(self):
@@ -154,8 +157,8 @@ 
    Source code for pina.callbacks.processing_callbacks
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/condition.html b/_modules/pina/condition.html
index 57c4f72d..119be3ae 100644
--- a/_modules/pina/condition.html
+++ b/_modules/pina/condition.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.condition — PINA 0.1 documentation
+  pina.condition — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -88,6 +90,7 @@
              
   
    Source code for pina.condition
     """ Condition module. """
+
 from .label_tensor import LabelTensor
 from .geometry import Location
 from .equation.equation import Equation
@@ -140,7 +143,11 @@ 
    Source code for pina.condition
         """
 
     __slots__ = [
-        'input_points', 'output_points', 'location', 'equation', 'data_weight'
+        "input_points",
+        "output_points",
+        "location",
+        "equation",
+        "data_weight",
     ]
 
     def _dictvalue_isinstance(self, dict_, key_, class_):
@@ -154,27 +161,28 @@ 
    Source code for pina.condition
             """
         Constructor for the `Condition` class.
         """
-        self.data_weight = kwargs.pop('data_weight', 1.0)
+        self.data_weight = kwargs.pop("data_weight", 1.0)
 
         if len(args) != 0:
             raise ValueError(
-                'Condition takes only the following keyword arguments: {`input_points`, `output_points`, `location`, `function`, `data_weight`}.'
+                f"Condition takes only the following keyword arguments: {Condition.__slots__}."
             )
 
-        if (sorted(kwargs.keys()) != sorted(['input_points', 'output_points'])
-                and sorted(kwargs.keys()) != sorted(['location', 'equation'])
-                and sorted(kwargs.keys()) != sorted(
-                    ['input_points', 'equation'])):
-            raise ValueError(f'Invalid keyword arguments {kwargs.keys()}.')
-
-        if not self._dictvalue_isinstance(kwargs, 'input_points', LabelTensor):
-            raise TypeError('`input_points` must be a torch.Tensor.')
-        if not self._dictvalue_isinstance(kwargs, 'output_points', LabelTensor):
-            raise TypeError('`output_points` must be a torch.Tensor.')
-        if not self._dictvalue_isinstance(kwargs, 'location', Location):
-            raise TypeError('`location` must be a Location.')
-        if not self._dictvalue_isinstance(kwargs, 'equation', Equation):
-            raise TypeError('`equation` must be a Equation.')
+        if (
+            sorted(kwargs.keys()) != sorted(["input_points", "output_points"])
+            and sorted(kwargs.keys()) != sorted(["location", "equation"])
+            and sorted(kwargs.keys()) != sorted(["input_points", "equation"])
+        ):
+            raise ValueError(f"Invalid keyword arguments {kwargs.keys()}.")
+
+        if not self._dictvalue_isinstance(kwargs, "input_points", LabelTensor):
+            raise TypeError("`input_points` must be a torch.Tensor.")
+        if not self._dictvalue_isinstance(kwargs, "output_points", LabelTensor):
+            raise TypeError("`output_points` must be a torch.Tensor.")
+        if not self._dictvalue_isinstance(kwargs, "location", Location):
+            raise TypeError("`location` must be a Location.")
+        if not self._dictvalue_isinstance(kwargs, "equation", Equation):
+            raise TypeError("`equation` must be a Equation.")
 
         for key, value in kwargs.items():
             setattr(self, key, value)
    
@@ -187,8 +195,8 @@ 
    Source code for pina.condition
       
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/equation/equation.html b/_modules/pina/equation/equation.html
index 4e572d41..cde26391 100644
--- a/_modules/pina/equation/equation.html
+++ b/_modules/pina/equation/equation.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.equation.equation — PINA 0.1 documentation
+  pina.equation.equation — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -88,6 +90,7 @@
              
   
    Source code for pina.equation.equation
     """ Module for Equation. """
+
 from .equation_interface import EquationInterface
 
 
@@ -104,12 +107,14 @@ 
    Source code for pina.equation.equation
             :type equation: Callable
         """
         if not callable(equation):
-            raise ValueError('equation must be a callable function.'
-                             'Expected a callable function, got '
-                             f'{equation}')
+            raise ValueError(
+                "equation must be a callable function."
+                "Expected a callable function, got "
+                f"{equation}"
+            )
         self.__equation = equation
 
-
    [docs]    def residual(self, input_, output_, params_ = None):
+
    [docs]    def residual(self, input_, output_, params_=None):
         """
         Residual computation of the equation.
 
@@ -141,8 +146,8 @@ 
    Source code for pina.equation.equation
       
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/equation/equation_factory.html b/_modules/pina/equation/equation_factory.html
index 0b388fb8..01132fc1 100644
--- a/_modules/pina/equation/equation_factory.html
+++ b/_modules/pina/equation/equation_factory.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.equation.equation_factory — PINA 0.1 documentation
+  pina.equation.equation_factory — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -88,6 +90,7 @@
              
   
    Source code for pina.equation.equation_factory
     """ Module """
+
 from .equation import Equation
 from ..operators import grad, div, laplacian
 
@@ -200,8 +203,8 @@ 
    Source code for pina.equation.equation_factory
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/equation/equation_interface.html b/_modules/pina/equation/equation_interface.html
index 5e04794c..d2929263 100644
--- a/_modules/pina/equation/equation_interface.html
+++ b/_modules/pina/equation/equation_interface.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.equation.equation_interface — PINA 0.1 documentation
+  pina.equation.equation_interface — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -88,6 +90,7 @@
              
   
    Source code for pina.equation.equation_interface
     """ Module for EquationInterface class """
+
 from abc import ABCMeta, abstractmethod
 
 
@@ -123,8 +126,8 @@ 
    Source code for pina.equation.equation_interface
    
   
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/equation/system_equation.html b/_modules/pina/equation/system_equation.html
index 5a3ef98b..81bcf26d 100644
--- a/_modules/pina/equation/system_equation.html
+++ b/_modules/pina/equation/system_equation.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.equation.system_equation — PINA 0.1 documentation
+  pina.equation.system_equation — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -88,6 +90,7 @@
              
   
    Source code for pina.equation.system_equation
     """ Module for SystemEquation. """
+
 import torch
 from .equation import Equation
 from ..utils import check_consistency
@@ -95,7 +98,7 @@ 
    Source code for pina.equation.system_equation
    [docs]class SystemEquation(Equation):
 
-    def __init__(self, list_equation, reduction='mean'):
+    def __init__(self, list_equation, reduction="mean"):
         """
         System of Equation class for specifing any system
         of equations in PINA.
@@ -122,15 +125,16 @@ 
    Source code for pina.equation.system_equation
    self.equations.append(Equation(equation))
 
         # possible reduction
-        if reduction == 'mean':
+        if reduction == "mean":
             self.reduction = torch.mean
-        elif reduction == 'sum':
+        elif reduction == "sum":
             self.reduction = torch.sum
-        elif (reduction == 'none') or callable(reduction):
+        elif (reduction == "none") or callable(reduction):
             self.reduction = reduction
         else:
             raise NotImplementedError(
-                'Only mean and sum reductions implemented.')
+                "Only mean and sum reductions implemented."
+            )
 
 
    [docs]    def residual(self, input_, output_, params_=None):
         """
@@ -153,9 +157,13 @@ 
    Source code for pina.equation.system_equation
            :rtype: LabelTensor
         """
         residual = torch.hstack(
-            [equation.residual(input_, output_, params_) for equation in self.equations])
+            [
+                equation.residual(input_, output_, params_)
+                for equation in self.equations
+            ]
+        )
 
-        if self.reduction == 'none':
+        if self.reduction == "none":
             return residual
 
         return self.reduction(residual, dim=-1)
    
@@ -168,8 +176,8 @@ 
    Source code for pina.equation.system_equation
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/geometry/cartesian.html b/_modules/pina/geometry/cartesian.html
index 5b308466..893c3906 100644
--- a/_modules/pina/geometry/cartesian.html
+++ b/_modules/pina/geometry/cartesian.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.geometry.cartesian — PINA 0.1 documentation
+  pina.geometry.cartesian — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -161,17 +163,17 @@ 
    Source code for pina.geometry.cartesian
             :rtype: torch.Tensor
         """
         dim = bounds.shape[0]
-        if mode in ['chebyshev', 'grid'] and dim != 1:
-            raise RuntimeError('Something wrong in Span...')
+        if mode in ["chebyshev", "grid"] and dim != 1:
+            raise RuntimeError("Something wrong in Span...")
 
-        if mode == 'random':
+        if mode == "random":
             pts = torch.rand(size=(n, dim))
-        elif mode == 'chebyshev':
-            pts = chebyshev_roots(n).mul(.5).add(.5).reshape(-1, 1)
-        elif mode == 'grid':
+        elif mode == "chebyshev":
+            pts = chebyshev_roots(n).mul(0.5).add(0.5).reshape(-1, 1)
+        elif mode == "grid":
             pts = torch.linspace(0, 1, n).reshape(-1, 1)
         # elif mode == 'lh' or mode == 'latin':
-        elif mode in ['lh', 'latin']:
+        elif mode in ["lh", "latin"]:
             pts = torch_lhs(n, dim)
 
         pts *= bounds[:, 1] - bounds[:, 0]
@@ -179,7 +181,7 @@ 
    Source code for pina.geometry.cartesian
     
         return pts
 
-
    [docs]    def sample(self, n, mode='random', variables='all'):
+
    [docs]    def sample(self, n, mode="random", variables="all"):
         """Sample routine.
 
         :param n: Number of points to sample, see Note below
@@ -234,7 +236,7 @@ 
    Source code for pina.geometry.cartesian
             """
 
         def _1d_sampler(n, mode, variables):
-            """ Sample independentely the variables and cross the results"""
+            """Sample independentely the variables and cross the results"""
             tmp = []
             for variable in variables:
                 if variable in self.range_.keys():
@@ -247,17 +249,18 @@ 
    Source code for pina.geometry.cartesian
     
             result = tmp[0]
             for i in tmp[1:]:
-                result = result.append(i, mode='cross')
+                result = result.append(i, mode="cross")
 
             for variable in variables:
                 if variable in self.fixed_.keys():
                     value = self.fixed_[variable]
-                    pts_variable = torch.tensor([[value]
-                                                 ]).repeat(result.shape[0], 1)
+                    pts_variable = torch.tensor([[value]]).repeat(
+                        result.shape[0], 1
+                    )
                     pts_variable = pts_variable.as_subclass(LabelTensor)
                     pts_variable.labels = [variable]
 
-                    result = result.append(pts_variable, mode='std')
+                    result = result.append(pts_variable, mode="std")
 
             return result
 
@@ -286,12 +289,13 @@ 
    Source code for pina.geometry.cartesian
                 for variable in variables:
                 if variable in self.fixed_.keys():
                     value = self.fixed_[variable]
-                    pts_variable = torch.tensor([[value]
-                                                 ]).repeat(result.shape[0], 1)
+                    pts_variable = torch.tensor([[value]]).repeat(
+                        result.shape[0], 1
+                    )
                     pts_variable = pts_variable.as_subclass(LabelTensor)
                     pts_variable.labels = [variable]
 
-                    result = result.append(pts_variable, mode='std')
+                    result = result.append(pts_variable, mode="std")
             return result
 
         def _single_points_sample(n, variables):
@@ -315,22 +319,22 @@ 
    Source code for pina.geometry.cartesian
     
             result = tmp[0]
             for i in tmp[1:]:
-                result = result.append(i, mode='std')
+                result = result.append(i, mode="std")
 
             return result
 
         if self.fixed_ and (not self.range_):
             return _single_points_sample(n, variables)
 
-        if variables == 'all':
+        if variables == "all":
             variables = list(self.range_.keys()) + list(self.fixed_.keys())
 
-        if mode in ['grid', 'chebyshev']:
+        if mode in ["grid", "chebyshev"]:
             return _1d_sampler(n, mode, variables)
-        elif mode in ['random', 'lh', 'latin']:
+        elif mode in ["random", "lh", "latin"]:
             return _Nd_sampler(n, mode, variables)
         else:
-            raise ValueError(f'mode={mode} is not valid.')
    
+            raise ValueError(f"mode={mode} is not valid.")
    
 
 
    [docs]    def is_inside(self, point, check_border=False):
         """Check if a point is inside the ellipsoid.
@@ -371,8 +375,8 @@ 
    Source code for pina.geometry.cartesian
       
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/geometry/difference_domain.html b/_modules/pina/geometry/difference_domain.html
index c0b954d3..2a5e7ec9 100644
--- a/_modules/pina/geometry/difference_domain.html
+++ b/_modules/pina/geometry/difference_domain.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.geometry.difference_domain — PINA 0.1 documentation
+  pina.geometry.difference_domain — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -109,7 +111,7 @@ 
    Source code for pina.geometry.difference_domain
    <
         the dimension of the geometry space.
 
         :param list geometries: A list of geometries from ``pina.geometry``
-            such as ``EllipsoidDomain`` or ``CartesianDomain``. The first 
+            such as ``EllipsoidDomain`` or ``CartesianDomain``. The first
             geometry in the list is the geometry from which points are
             sampled. The rest of the geometries are the geometries that
             are excluded from the first geometry to find the difference.
@@ -128,7 +130,7 @@ 
    Source code for pina.geometry.difference_domain
    <
         Check if a point is inside the ``Difference`` domain.
 
         :param point: Point to be checked.
-        :type point: torch.Tensor   
+        :type point: torch.Tensor
         :param bool check_border: If ``True``, the border is considered inside.
         :return: ``True`` if the point is inside the Exclusion domain, ``False`` otherwise.
         :rtype: bool
@@ -138,7 +140,7 @@ 
    Source code for pina.geometry.difference_domain
    <
                 return False
         return self.geometries[0].is_inside(point, check_border)
    
 
-
    [docs]    def sample(self, n, mode='random', variables='all'):
+
    [docs]    def sample(self, n, mode="random", variables="all"):
         """
         Sample routine for ``Difference`` domain.
 
@@ -166,9 +168,10 @@ 
    Source code for pina.geometry.difference_domain
    <
                 5
 
         """
-        if mode != 'random':
+        if mode != "random":
             raise NotImplementedError(
-                f'{mode} is not a valid mode for sampling.')
+                f"{mode} is not a valid mode for sampling."
+            )
 
         sampled = []
 
@@ -198,8 +201,8 @@ 
    Source code for pina.geometry.difference_domain
    <
   
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/geometry/ellipsoid.html b/_modules/pina/geometry/ellipsoid.html
index f9d4f06e..30096819 100644
--- a/_modules/pina/geometry/ellipsoid.html
+++ b/_modules/pina/geometry/ellipsoid.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.geometry.ellipsoid — PINA 0.1 documentation
+  pina.geometry.ellipsoid — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -174,7 +176,7 @@ 
    Source code for pina.geometry.ellipsoid
     
         .. note::
             When ``sample_surface`` in the ``__init()__``
-            is set to ``True``, then the method only checks 
+            is set to ``True``, then the method only checks
             points on the surface, and not inside the domain.
 
         :param point: Point to be checked.
@@ -192,7 +194,7 @@ 
    Source code for pina.geometry.ellipsoid
             # get axis ellipse as tensors
         list_dict_vals = list(self._axis.values())
         tmp = torch.tensor(list_dict_vals, dtype=torch.float)
-        ax_sq = LabelTensor(tmp.reshape(1, -1)**2, self.variables)
+        ax_sq = LabelTensor(tmp.reshape(1, -1) ** 2, self.variables)
 
         # get centers ellipse as tensors
         list_dict_vals = list(self._centers.values())
@@ -200,16 +202,18 @@ 
    Source code for pina.geometry.ellipsoid
             centers = LabelTensor(tmp.reshape(1, -1), self.variables)
 
         if not all([i in ax_sq.labels for i in point.labels]):
-            raise ValueError('point labels different from constructor'
-                             f' dictionary labels. Got {point.labels},'
-                             f' expected {ax_sq.labels}.')
+            raise ValueError(
+                "point labels different from constructor"
+                f" dictionary labels. Got {point.labels},"
+                f" expected {ax_sq.labels}."
+            )
 
         # point square + shift center
         point_sq = (point - centers).pow(2)
         point_sq.labels = point.labels
 
         # calculate ellispoid equation
-        eqn = torch.sum(point_sq.extract(ax_sq.labels) / ax_sq) - 1.
+        eqn = torch.sum(point_sq.extract(ax_sq.labels) / ax_sq) - 1.0
 
         # if we have sampled only the surface, we check that the
         # point is inside the surface border only
@@ -249,8 +253,9 @@ 
    Source code for pina.geometry.ellipsoid
             dim = len(variables)
 
         # get values center
-        pairs_center = [(k, v) for k, v in self._centers.items()
-                        if k in variables]
+        pairs_center = [
+            (k, v) for k, v in self._centers.items() if k in variables
+        ]
         _, values_center = map(list, zip(*pairs_center))
         values_center = torch.tensor(values_center)
 
@@ -260,7 +265,7 @@ 
    Source code for pina.geometry.ellipsoid
             values_axis = torch.tensor(values_axis)
 
         # Sample in the unit sphere
-        if mode == 'random':
+        if mode == "random":
             # 1. Sample n points from the surface of a unit sphere
             # 2. Scale each dimension using torch.rand()
             #    (a random number between 0-1) so that it lies within
@@ -281,7 +286,7 @@ 
    Source code for pina.geometry.ellipsoid
     
         return pts
 
-
    [docs]    def sample(self, n, mode='random', variables='all'):
+
    [docs]    def sample(self, n, mode="random", variables="all"):
         """Sample routine.
 
         :param int n: Number of points to sample in the shape.
@@ -327,12 +332,13 @@ 
    Source code for pina.geometry.ellipsoid
                 for variable in variables:
                 if variable in self.fixed_.keys():
                     value = self.fixed_[variable]
-                    pts_variable = torch.tensor([[value]
-                                                 ]).repeat(result.shape[0], 1)
+                    pts_variable = torch.tensor([[value]]).repeat(
+                        result.shape[0], 1
+                    )
                     pts_variable = pts_variable.as_subclass(LabelTensor)
                     pts_variable.labels = [variable]
 
-                    result = result.append(pts_variable, mode='std')
+                    result = result.append(pts_variable, mode="std")
             return result
 
         def _single_points_sample(n, variables):
@@ -356,20 +362,20 @@ 
    Source code for pina.geometry.ellipsoid
     
             result = tmp[0]
             for i in tmp[1:]:
-                result = result.append(i, mode='std')
+                result = result.append(i, mode="std")
 
             return result
 
         if self.fixed_ and (not self.range_):
             return _single_points_sample(n, variables)
 
-        if variables == 'all':
+        if variables == "all":
             variables = list(self.range_.keys()) + list(self.fixed_.keys())
 
-        if mode in ['random']:
+        if mode in ["random"]:
             return _Nd_sampler(n, mode, variables)
         else:
-            raise NotImplementedError(f'mode={mode} is not implemented.')
    
+            raise NotImplementedError(f"mode={mode} is not implemented.")
    
 
    
 
            
    
@@ -379,8 +385,8 @@ 
    Source code for pina.geometry.ellipsoid
       
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/geometry/exclusion_domain.html b/_modules/pina/geometry/exclusion_domain.html
index d2093606..c43ad680 100644
--- a/_modules/pina/geometry/exclusion_domain.html
+++ b/_modules/pina/geometry/exclusion_domain.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.geometry.exclusion_domain — PINA 0.1 documentation
+  pina.geometry.exclusion_domain — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -126,7 +128,7 @@ 
    Source code for pina.geometry.exclusion_domain
            Check if a point is inside the ``Exclusion`` domain.
 
         :param point: Point to be checked.
-        :type point: torch.Tensor   
+        :type point: torch.Tensor
         :param bool check_border: If ``True``, the border is considered inside.
         :return: ``True`` if the point is inside the Exclusion domain, ``False`` otherwise.
         :rtype: bool
@@ -137,7 +139,7 @@ 
    Source code for pina.geometry.exclusion_domain
    flag += 1
         return flag == 1
    
 
-
    [docs]    def sample(self, n, mode='random', variables='all'):
+
    [docs]    def sample(self, n, mode="random", variables="all"):
         """
         Sample routine for ``Exclusion`` domain.
 
@@ -165,9 +167,10 @@ 
    Source code for pina.geometry.exclusion_domain
                    5
 
         """
-        if mode != 'random':
+        if mode != "random":
             raise NotImplementedError(
-                f'{mode} is not a valid mode for sampling.')
+                f"{mode} is not a valid mode for sampling."
+            )
 
         sampled = []
 
@@ -203,8 +206,8 @@ 
    Source code for pina.geometry.exclusion_domain
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/geometry/intersection_domain.html b/_modules/pina/geometry/intersection_domain.html
index f09adb24..38046422 100644
--- a/_modules/pina/geometry/intersection_domain.html
+++ b/_modules/pina/geometry/intersection_domain.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.geometry.intersection_domain — PINA 0.1 documentation
+  pina.geometry.intersection_domain — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -109,7 +111,7 @@ 
    Source code for pina.geometry.intersection_domain
            with :math:`x` a point in :math:`\mathbb{R}^N` and :math:`N`
         the dimension of the geometry space.
 
-        :param list geometries: A list of geometries from ``pina.geometry`` 
+        :param list geometries: A list of geometries from ``pina.geometry``
             such as ``EllipsoidDomain`` or ``CartesianDomain``. The intersection
             will be taken between all the geometries in the list. The resulting
             geometry will be the intersection of all the geometries in the list.
@@ -128,7 +130,7 @@ 
    Source code for pina.geometry.intersection_domain
            Check if a point is inside the ``Intersection`` domain.
 
         :param point: Point to be checked.
-        :type point: torch.Tensor   
+        :type point: torch.Tensor
         :param bool check_border: If ``True``, the border is considered inside.
         :return: ``True`` if the point is inside the Intersection domain, ``False`` otherwise.
         :rtype: bool
@@ -139,7 +141,7 @@ 
    Source code for pina.geometry.intersection_domain
    flag += 1
         return flag == len(self.geometries)
    
 
-
    [docs]    def sample(self, n, mode='random', variables='all'):
+
    [docs]    def sample(self, n, mode="random", variables="all"):
         """
         Sample routine for ``Intersection`` domain.
 
@@ -167,9 +169,10 @@ 
    Source code for pina.geometry.intersection_domain
                    5
 
         """
-        if mode != 'random':
+        if mode != "random":
             raise NotImplementedError(
-                f'{mode} is not a valid mode for sampling.')
+                f"{mode} is not a valid mode for sampling."
+            )
 
         sampled = []
 
@@ -204,8 +207,8 @@ 
    Source code for pina.geometry.intersection_domain
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/geometry/location.html b/_modules/pina/geometry/location.html
index 19c07dcb..154b98cf 100644
--- a/_modules/pina/geometry/location.html
+++ b/_modules/pina/geometry/location.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.geometry.location — PINA 0.1 documentation
+  pina.geometry.location — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -127,8 +129,8 @@ 
    Source code for pina.geometry.location
       
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/geometry/operation_interface.html b/_modules/pina/geometry/operation_interface.html
index 78eb93a0..b1952645 100644
--- a/_modules/pina/geometry/operation_interface.html
+++ b/_modules/pina/geometry/operation_interface.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.geometry.operation_interface — PINA 0.1 documentation
+  pina.geometry.operation_interface — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -115,7 +117,7 @@ 
    Source code for pina.geometry.operation_interface
    @property
     def geometries(self):
-        """ 
+        """
         The geometries to perform set operation.
         """
         return self._geometries
@@ -129,15 +131,15 @@ 
    Source code for pina.geometry.operation_interface
            :rtype: list[str]
         """
         return self.geometries[0].variables
-    
-
    [docs]    @ abstractmethod
+
+
    [docs]    @abstractmethod
     def is_inside(self, point, check_border=False):
         """
         Check if a point is inside the resulting domain after
         a set operation is applied.
 
         :param point: Point to be checked.
-        :type point: torch.Tensor   
+        :type point: torch.Tensor
         :param bool check_border: If ``True``, the border is considered inside.
         :return: ``True`` if the point is inside the Intersection domain, ``False`` otherwise.
         :rtype: bool
@@ -153,7 +155,8 @@ 
    Source code for pina.geometry.operation_interface
    for geometry in geometries:
             if geometry.variables != geometries[0].variables:
                 raise NotImplementedError(
-                    f'The geometries need to have same dimensions and labels.')
    
+                    f"The geometries need to have same dimensions and labels."
+                )
    
 
    
 
            
    
@@ -163,8 +166,8 @@ 
    Source code for pina.geometry.operation_interface
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/geometry/simplex.html b/_modules/pina/geometry/simplex.html
index 49d873ed..28b5daf9 100644
--- a/_modules/pina/geometry/simplex.html
+++ b/_modules/pina/geometry/simplex.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.geometry.simplex — PINA 0.1 documentation
+  pina.geometry.simplex — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -183,7 +185,7 @@ 
    Source code for pina.geometry.simplex
                 # respective coord bounded by the lowest and highest values
             span_dict[coord] = [
                 float(sorted_vertices[0][i]),
-                float(sorted_vertices[-1][i])
+                float(sorted_vertices[-1][i]),
             ]
 
         return CartesianDomain(span_dict)
@@ -209,16 +211,19 @@ 
    Source code for pina.geometry.simplex
             """
 
         if not all(label in self.variables for label in point.labels):
-            raise ValueError("Point labels different from constructor"
-                             f" dictionary labels. Got {point.labels},"
-                             f" expected {self.variables}.")
+            raise ValueError(
+                "Point labels different from constructor"
+                f" dictionary labels. Got {point.labels},"
+                f" expected {self.variables}."
+            )
 
         point_shift = point - self._vertices_matrix[-1]
         point_shift = point_shift.tensor.reshape(-1, 1)
 
         # compute barycentric coordinates
-        lambda_ = torch.linalg.solve(self._vectors_shifted * 1.0,
-                                     point_shift * 1.0)
+        lambda_ = torch.linalg.solve(
+            self._vectors_shifted * 1.0, point_shift * 1.0
+        )
         lambda_1 = 1.0 - torch.sum(lambda_)
         lambdas = torch.vstack([lambda_, lambda_1])
 
@@ -226,8 +231,9 @@ 
    Source code for pina.geometry.simplex
             if not check_border:
             return all(torch.gt(lambdas, 0.0)) and all(torch.lt(lambdas, 1.0))
 
-        return all(torch.ge(lambdas, 0)) and (any(torch.eq(lambdas, 0))
-                                              or any(torch.eq(lambdas, 1)))
    
+        return all(torch.ge(lambdas, 0)) and (
+            any(torch.eq(lambdas, 0)) or any(torch.eq(lambdas, 1))
+        )
    
 
     def _sample_interior_randomly(self, n, variables):
         """
@@ -252,9 +258,9 @@ 
    Source code for pina.geometry.simplex
     
         sampled_points = []
         while len(sampled_points) < n:
-            sampled_point = self._cartesian_bound.sample(n=1,
-                                                         mode="random",
-                                                         variables=variables)
+            sampled_point = self._cartesian_bound.sample(
+                n=1, mode="random", variables=variables
+            )
 
             if self.is_inside(sampled_point, self._sample_surface):
                 sampled_points.append(sampled_point)
@@ -285,9 +291,9 @@ 
    Source code for pina.geometry.simplex
                 # extract number of vertices
             number_of_vertices = self._vertices_matrix.shape[0]
             # extract idx lambda to set to zero randomly
-            idx_lambda = torch.randint(low=0,
-                                       high=number_of_vertices,
-                                       size=(1, ))
+            idx_lambda = torch.randint(
+                low=0, high=number_of_vertices, size=(1,)
+            )
             # build lambda vector
             # 1. sampling [1, 2)
             lambdas = torch.rand((number_of_vertices, 1))
@@ -335,8 +341,8 @@ 
    Source code for pina.geometry.simplex
       
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/geometry/union_domain.html b/_modules/pina/geometry/union_domain.html
index 0be8e2f5..7cdc17d6 100644
--- a/_modules/pina/geometry/union_domain.html
+++ b/_modules/pina/geometry/union_domain.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.geometry.union_domain — PINA 0.1 documentation
+  pina.geometry.union_domain — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -109,7 +111,7 @@ 
    Source code for pina.geometry.union_domain
             with :math:`x` a point in :math:`\mathbb{R}^N` and :math:`N`
         the dimension of the geometry space.
 
-        :param list geometries: A list of geometries from ``pina.geometry`` 
+        :param list geometries: A list of geometries from ``pina.geometry``
             such as ``EllipsoidDomain`` or ``CartesianDomain``.
 
         :Example:
@@ -139,7 +141,7 @@ 
    Source code for pina.geometry.union_domain
                     return True
         return False
    
 
-
    [docs]    def sample(self, n, mode='random', variables='all'):
+
    [docs]    def sample(self, n, mode="random", variables="all"):
         """
         Sample routine for ``Union`` domain.
 
@@ -182,8 +184,10 @@ 
    Source code for pina.geometry.union_domain
                 # different than zero. Notice that len(geometries) is
             # always smaller than remaider.
             sampled_points.append(
-                geometry.sample(num_points + int(i < remainder), mode,
-                                variables))
+                geometry.sample(
+                    num_points + int(i < remainder), mode, variables
+                )
+            )
             # in case number of sampled points is smaller than the number of geometries
             if len(sampled_points) >= n:
                 break
@@ -198,8 +202,8 @@ 
    Source code for pina.geometry.union_domain
       
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/label_tensor.html b/_modules/pina/label_tensor.html
index 0d8c2f34..50d5353a 100644
--- a/_modules/pina/label_tensor.html
+++ b/_modules/pina/label_tensor.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.label_tensor — PINA 0.1 documentation
+  pina.label_tensor — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -88,6 +90,7 @@
              
   
    Source code for pina.label_tensor
     """ Module for LabelTensor """
+
 from typing import Any
 import torch
 from torch import Tensor
@@ -101,7 +104,7 @@ 
    Source code for pina.label_tensor
             return super().__new__(cls, x, *args, **kwargs)
 
     def __init__(self, x, labels):
-        '''
+        """
         Construct a `LabelTensor` by passing a tensor and a list of column
         labels. Such labels uniquely identify the columns of the tensor,
         allowing for an easier manipulation.
@@ -153,7 +156,7 @@ 
    Source code for pina.label_tensor
                         [0.9427, 0.5819],
                     [0.9518, 0.1025],
                     [0.8066, 0.9615]])
-        '''
+        """
         if x.ndim == 1:
             x = x.reshape(-1, 1)
 
@@ -161,10 +164,12 @@ 
    Source code for pina.label_tensor
                 labels = [labels]
 
         if len(labels) != x.shape[-1]:
-            raise ValueError('the tensor has not the same number of columns of '
-                             'the passed labels.')
+            raise ValueError(
+                "the tensor has not the same number of columns of "
+                "the passed labels."
+            )
         self._labels = labels
-    
+
     @property
     def labels(self):
         """Property decorator for labels
@@ -177,8 +182,10 @@ 
    Source code for pina.label_tensor
         @labels.setter
     def labels(self, labels):
         if len(labels) != self.shape[self.ndim - 1]:  # small check
-            raise ValueError('The tensor has not the same number of columns of '
-                             'the passed labels.')
+            raise ValueError(
+                "The tensor has not the same number of columns of "
+                "the passed labels."
+            )
 
         self._labels = labels  # assign the label
 
@@ -198,7 +205,7 @@ 
    Source code for pina.label_tensor
     
         all_labels = [label for lt in label_tensors for label in lt.labels]
         if set(all_labels) != set(label_tensors[0].labels):
-            raise RuntimeError('The tensors to stack have different labels')
+            raise RuntimeError("The tensors to stack have different labels")
 
         labels = label_tensors[0].labels
         tensors = [lt.extract(labels) for lt in label_tensors]
@@ -212,7 +219,7 @@ 
    Source code for pina.label_tensor
             :return: A copy of the tensor.
         :rtype: LabelTensor
         """
-        # # used before merging 
+        # # used before merging
         # try:
         #     out = LabelTensor(super().clone(*args, **kwargs), self.labels)
         # except:
@@ -273,14 +280,15 @@ 
    Source code for pina.label_tensor
                 pass
         else:
             raise TypeError(
-                '`label_to_extract` should be a str, or a str iterator')
+                "`label_to_extract` should be a str, or a str iterator"
+            )
 
         indeces = []
         for f in label_to_extract:
             try:
                 indeces.append(self.labels.index(f))
             except ValueError:
-                raise ValueError(f'`{f}` not in the labels list')
+                raise ValueError(f"`{f}` not in the labels list")
 
         new_data = super(Tensor, self.T).__getitem__(indeces).T
         new_labels = [self.labels[idx] for idx in indeces]
@@ -292,17 +300,16 @@ 
    Source code for pina.label_tensor
     
 
    [docs]    def detach(self):
         detached = super().detach()
-        if hasattr(self, '_labels'):
+        if hasattr(self, "_labels"):
             detached._labels = self._labels
         return detached
    
 
-
-
    [docs]    def requires_grad_(self, mode = True):
+
    [docs]    def requires_grad_(self, mode=True):
         lt = super().requires_grad_(mode)
         lt.labels = self.labels
         return lt
    
 
-
    [docs]    def append(self, lt, mode='std'):
+
    [docs]    def append(self, lt, mode="std"):
         """
         Return a copy of the merged tensors.
 
@@ -312,22 +319,23 @@ 
    Source code for pina.label_tensor
             :rtype: LabelTensor
         """
         if set(self.labels).intersection(lt.labels):
-            raise RuntimeError('The tensors to merge have common labels')
+            raise RuntimeError("The tensors to merge have common labels")
 
         new_labels = self.labels + lt.labels
-        if mode == 'std':
+        if mode == "std":
             new_tensor = torch.cat((self, lt), dim=1)
-        elif mode == 'first':
+        elif mode == "first":
             raise NotImplementedError
-        elif mode == 'cross':
+        elif mode == "cross":
             tensor1 = self
             tensor2 = lt
             n1 = tensor1.shape[0]
             n2 = tensor2.shape[0]
 
             tensor1 = LabelTensor(tensor1.repeat(n2, 1), labels=tensor1.labels)
-            tensor2 = LabelTensor(tensor2.repeat_interleave(n1, dim=0),
-                                  labels=tensor2.labels)
+            tensor2 = LabelTensor(
+                tensor2.repeat_interleave(n1, dim=0), labels=tensor2.labels
+            )
             new_tensor = torch.cat((tensor1, tensor2), dim=1)
 
         new_tensor = new_tensor.as_subclass(LabelTensor)
@@ -339,34 +347,37 @@ 
    Source code for pina.label_tensor
             Return a copy of the selected tensor.
         """
 
-        if isinstance(index, str) or (isinstance(index, (tuple, list))and all(isinstance(a, str) for a in index)):
+        if isinstance(index, str) or (
+            isinstance(index, (tuple, list))
+            and all(isinstance(a, str) for a in index)
+        ):
             return self.extract(index)
 
         selected_lt = super(Tensor, self).__getitem__(index)
-        
+
         try:
             len_index = len(index)
         except TypeError:
             len_index = 1
-        
+
         if isinstance(index, int) or len_index == 1:
             if selected_lt.ndim == 1:
                 selected_lt = selected_lt.reshape(1, -1)
-            if hasattr(self, 'labels'):
+            if hasattr(self, "labels"):
                 selected_lt.labels = self.labels
         elif len_index == 2:
             if selected_lt.ndim == 1:
                 selected_lt = selected_lt.reshape(-1, 1)
-            if hasattr(self, 'labels'):
+            if hasattr(self, "labels"):
                 if isinstance(index[1], list):
                     selected_lt.labels = [self.labels[i] for i in index[1]]
                 else:
                     selected_lt.labels = self.labels[index[1]]
         else:
             selected_lt.labels = self.labels
-                    
+
         return selected_lt
-    
+
     @property
     def tensor(self):
         return self.as_subclass(Tensor)
@@ -375,10 +386,10 @@ 
    Source code for pina.label_tensor
             return super().__len__()
 
     def __str__(self):
-        if hasattr(self, 'labels'):
-            s = f'labels({str(self.labels)})\n'
+        if hasattr(self, "labels"):
+            s = f"labels({str(self.labels)})\n"
         else:
-            s = 'no labels\n'
+            s = "no labels\n"
         s += super().__str__()
         return s
    
 
    
@@ -390,8 +401,8 @@ 
    Source code for pina.label_tensor
       
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/loss.html b/_modules/pina/loss.html
index 44382863..aed17588 100644
--- a/_modules/pina/loss.html
+++ b/_modules/pina/loss.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.loss — PINA 0.1 documentation
+  pina.loss — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -94,7 +96,7 @@ 
    Source code for pina.loss
     import torch
 from .utils import check_consistency
 
-__all__ = ['LossInterface', 'LpLoss', 'PowerLoss']
+__all__ = ["LossInterface", "LpLoss", "PowerLoss"]
 
 
 
    [docs]class LossInterface(_Loss, metaclass=ABCMeta):
@@ -103,10 +105,10 @@ 
    Source code for pina.loss
         should be inheritied from this class.
     """
 
-    def __init__(self, reduction='mean'):
+    def __init__(self, reduction="mean"):
         """
         :param str reduction: Specifies the reduction to apply to the output:
-            ``none`` | ``mean`` | ``sum``. When ``none``: no reduction 
+            ``none`` | ``mean`` | ``sum``. When ``none``: no reduction
             will be applied, ``mean``: the sum of the output will be divided
             by the number of elements in the output, ``sum``: the output will
             be summed. Note: ``size_average`` and ``reduce`` are in the
@@ -130,7 +132,7 @@ 
    Source code for pina.loss
             """Simple helper function to check reduction
 
         :param reduction: Specifies the reduction to apply to the output:
-            ``none`` | ``mean`` | ``sum``. When ``none``: no reduction 
+            ``none`` | ``mean`` | ``sum``. When ``none``: no reduction
             will be applied, ``mean``: the sum of the output will be divided
             by the number of elements in the output, ``sum``: the output will
             be summed. Note: ``size_average`` and ``reduce`` are in the
@@ -190,14 +192,14 @@ 
    Source code for pina.loss
         The division by :math:`n` can be avoided if one sets ``reduction`` to ``sum``.
     """
 
-    def __init__(self, p=2, reduction='mean', relative=False):
+    def __init__(self, p=2, reduction="mean", relative=False):
         """
         :param int p: Degree of Lp norm. It specifies the type of norm to
             be calculated. See `list of possible orders in torch linalg
             <https://pytorch.org/docs/stable/generated/torch.linalg.norm.html#torch.linalg.norm>`_ to
             for possible degrees. Default 2 (euclidean norm).
         :param str reduction: Specifies the reduction to apply to the output:
-            ``none`` | ``mean`` | ``sum``. ``none``: no reduction 
+            ``none`` | ``mean`` | ``sum``. ``none``: no reduction
             will be applied, ``mean``: the sum of the output will be divided
             by the number of elements in the output, ``sum``: the output will
             be summed.
@@ -206,7 +208,7 @@ 
    Source code for pina.loss
             super().__init__(reduction=reduction)
 
         # check consistency
-        check_consistency(p, (str,int,float))
+        check_consistency(p, (str, int, float))
         check_consistency(relative, bool)
 
         self.p = p
@@ -263,14 +265,14 @@ 
    Source code for pina.loss
         The division by :math:`n` can be avoided if one sets ``reduction`` to ``sum``.
     """
 
-    def __init__(self, p=2, reduction='mean', relative=False):
+    def __init__(self, p=2, reduction="mean", relative=False):
         """
         :param int p: Degree of Lp norm. It specifies the type of norm to
             be calculated. See `list of possible orders in torch linalg
             <https://pytorch.org/docs/stable/generated/torch.linalg.norm.html#torch.linalg.norm>`_ to
             see the possible degrees. Default 2 (euclidean norm).
         :param str reduction: Specifies the reduction to apply to the output:
-            ``none`` | ``mean`` | ``sum``. When ``none``: no reduction 
+            ``none`` | ``mean`` | ``sum``. When ``none``: no reduction
             will be applied, ``mean``: the sum of the output will be divided
             by the number of elements in the output, ``sum``: the output will
             be summed.
@@ -305,8 +307,8 @@ 
    Source code for pina.loss
       
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/model/base_no.html b/_modules/pina/model/base_no.html
new file mode 100644
index 00000000..a35f643c
--- /dev/null
+++ b/_modules/pina/model/base_no.html
@@ -0,0 +1,260 @@
+
+
+
+  
+  
+  pina.model.base_no — PINA 0.1.0.post2403 documentation
+    
+      
+
+  
+  
+  
+        
+        
+        
+        
+        
+        
+        
+    
+    
+     
+
+
+ 
+  
    
+    
+
+    
    
+
+      
    
+        
    
+          
    
+  
+  
    
+
    
+          
    
+           
    
+             
+  
    Source code for pina.model.base_no
    +"""
+Kernel Neural Operator Module.
+"""
+
+import torch
+from pina.utils import check_consistency
+
+
+
    [docs]class KernelNeuralOperator(torch.nn.Module):
+    r"""
+    Base class for composing Neural Operators with integral kernels.
+
+    This is a base class for composing neural operators with multiple
+    integral kernels. All neural operator models defined in PINA inherit
+    from this class. The structure is inspired by the work of Kovachki, N.
+    et al. see Figure 2 of the reference for extra details. The Neural
+    Operators inheriting from this class can be written as:
+
+    .. math::
+        G_\theta  := P \circ K_m \circ \cdot \circ K_1 \circ L
+
+    where:
+
+    *   :math:`G_\theta: \mathcal{A}\subset \mathbb{R}^{\rm{in}} \rightarrow
+        \mathcal{D}\subset \mathbb{R}^{\rm{out}}` is the neural operator
+        approximation of the unknown real operator :math:`G`, that is
+        :math:`G \approx G_\theta`
+    *   :math:`L: \mathcal{A}\subset \mathbb{R}^{\rm{in}} \rightarrow
+        \mathbb{R}^{\rm{emb}}` is a lifting operator mapping the input
+        from its domain :math:`\mathcal{A}\subset \mathbb{R}^{\rm{in}}`
+        to its embedding dimension :math:`\mathbb{R}^{\rm{emb}}`
+    *   :math:`\{K_i : \mathbb{R}^{\rm{emb}} \rightarrow
+        \mathbb{R}^{\rm{emb}} \}_{i=1}^m` are :math:`m` integral kernels
+        mapping each hidden representation to the next one.
+    *   :math:`P : \mathbb{R}^{\rm{emb}} \rightarrow  \mathcal{D}\subset
+        \mathbb{R}^{\rm{out}}` is a projection operator mapping the hidden
+        representation to the output function.
+
+    .. seealso::
+
+        **Original reference**: Kovachki, N., Li, Z., Liu, B.,
+        Azizzadenesheli, K., Bhattacharya, K., Stuart, A., & Anandkumar, A.
+        (2023). *Neural operator: Learning maps between function
+        spaces with applications to PDEs*. Journal of Machine Learning
+        Research, 24(89), 1-97.
+    """
+
+    def __init__(self, lifting_operator, integral_kernels, projection_operator):
+        """
+        :param torch.nn.Module lifting_operator: The lifting operator
+            mapping the input to its hidden dimension.
+        :param torch.nn.Module integral_kernels: List of integral kernels
+            mapping each hidden representation to the next one.
+        :param torch.nn.Module projection_operator: The projection operator
+            mapping the hidden representation to the output function.
+        """
+
+        super().__init__()
+
+        self._lifting_operator = lifting_operator
+        self._integral_kernels = integral_kernels
+        self._projection_operator = projection_operator
+
+    @property
+    def lifting_operator(self):
+        """
+        The lifting operator property.
+        """
+        return self._lifting_operator
+
+    @lifting_operator.setter
+    def lifting_operator(self, value):
+        """
+        The lifting operator setter
+
+        :param torch.nn.Module value: The lifting operator torch module.
+        """
+        check_consistency(value, torch.nn.Module)
+        self._lifting_operator = value
+
+    @property
+    def projection_operator(self):
+        """
+        The projection operator property.
+        """
+        return self._projection_operator
+
+    @projection_operator.setter
+    def projection_operator(self, value):
+        """
+        The projection operator setter
+
+        :param torch.nn.Module value: The projection operator torch module.
+        """
+        check_consistency(value, torch.nn.Module)
+        self._projection_operator = value
+
+    @property
+    def integral_kernels(self):
+        """
+        The integral kernels operator property.
+        """
+        return self._integral_kernels
+
+    @integral_kernels.setter
+    def integral_kernels(self, value):
+        """
+        The integral kernels operator setter
+
+        :param torch.nn.Module value: The integral kernels operator torch
+            module.
+        """
+        check_consistency(value, torch.nn.Module)
+        self._integral_kernels = value
+
+
    [docs]    def forward(self, x):
+        r"""
+        Forward computation for Base Neural Operator. It performs a
+        lifting of the input by the ``lifting_operator``.
+        Then different layers integral kernels are applied using
+        ``integral_kernels``. Finally the output is projected
+        to the final dimensionality by the ``projection_operator``.
+
+        :param torch.Tensor x: The input tensor for performing the
+            computation. It expects a tensor :math:`B \times N \times D`,
+            where :math:`B` is the batch_size, :math:`N` the number of points
+            in the mesh, :math:`D` the dimension of the problem. In particular
+            :math:`D` is the number of spatial/paramtric/temporal variables
+            plus the field variables. For example for 2D problems with 2
+            output\ variables :math:`D=4`.
+        :return: The output tensor obtained from the NO.
+        :rtype: torch.Tensor
+        """
+        x = self.lifting_operator(x)
+        x = self.integral_kernels(x)
+        x = self.projection_operator(x)
+        return x
    
+
    
+
+           
    
+          
    
+          
    
+
+  
    
+
+  
    
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
+      
    
+  
    
+
+  Built with Sphinx using a
+    theme
+    provided by Read the Docs.
+   
+
+
    
+        
    
+      
    
+    
    
+  
    
+   
+
+
+
\ No newline at end of file
diff --git a/_modules/pina/model/deeponet.html b/_modules/pina/model/deeponet.html
index 91149417..e8fb1517 100644
--- a/_modules/pina/model/deeponet.html
+++ b/_modules/pina/model/deeponet.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.model.deeponet — PINA 0.1 documentation
+  pina.model.deeponet — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
    
@@ -88,6 +90,7 @@
              
   
    Source code for pina.model.deeponet
     """Module for DeepONet model"""
+
 import torch
 import torch.nn as nn
 from ..utils import check_consistency, is_function
@@ -113,12 +116,14 @@ 
    Source code for pina.model.deeponet
     
     """
 
-    def __init__(self,
-                 networks,
-                 aggregator="*",
-                 reduction="+",
-                 scale=True,
-                 translation=True):
+    def __init__(
+        self,
+        networks,
+        aggregator="*",
+        reduction="+",
+        scale=True,
+        translation=True,
+    ):
         """
         :param dict networks: The neural networks to use as
             models. The ``dict`` takes as key a neural network, and
@@ -210,8 +215,9 @@ 
    Source code for pina.model.deeponet
                 shapes.append(key(input_).shape[-1])
 
         if not all(map(lambda x: x == shapes[0], shapes)):
-            raise ValueError('The passed networks have not the same '
-                             'output dimension.')
+            raise ValueError(
+                "The passed networks have not the same " "output dimension."
+            )
 
         # assign trunk and branch net with their input indeces
         self.models = torch.nn.ModuleList(networks.keys())
@@ -222,10 +228,16 @@ 
    Source code for pina.model.deeponet
             self._init_reduction(reduction=reduction)
 
         # scale and translation
-        self._scale = torch.nn.Parameter(torch.tensor(
-            [1.0])) if scale else torch.tensor([1.0])
-        self._trasl = torch.nn.Parameter(torch.tensor(
-            [1.0])) if translation else torch.tensor([1.0])
+        self._scale = (
+            torch.nn.Parameter(torch.tensor([1.0]))
+            if scale
+            else torch.tensor([1.0])
+        )
+        self._trasl = (
+            torch.nn.Parameter(torch.tensor([1.0]))
+            if translation
+            else torch.tensor([1.0])
+        )
 
     @staticmethod
     def _symbol_functions(**kwargs):
@@ -269,16 +281,18 @@ 
    Source code for pina.model.deeponet
                     return x.extract(indeces)
             except AttributeError:
                 raise RuntimeError(
-                    'Not possible to extract input variables from tensor.'
-                    ' Ensure that the passed tensor is a LabelTensor or'
-                    ' pass list of integers to extract variables. For'
-                    ' more information refer to warning in the documentation.')
+                    "Not possible to extract input variables from tensor."
+                    " Ensure that the passed tensor is a LabelTensor or"
+                    " pass list of integers to extract variables. For"
+                    " more information refer to warning in the documentation."
+                )
         elif isinstance(indeces[0], int):
             return x[..., indeces]
         else:
             raise RuntimeError(
-                'Not able to extract right indeces for tensor.'
-                ' For more information refer to warning in the documentation.')
+                "Not able to extract right indeces for tensor."
+                " For more information refer to warning in the documentation."
+            )
 
 
    [docs]    def forward(self, x):
         """
@@ -286,7 +300,7 @@ 
    Source code for pina.model.deeponet
     
         :param LabelTensor or torch.Tensor x: The input tensor for the forward call.
         :return: The output computed by the DeepONet model.
-        :rtype: LabelTensor or torch.Tensor 
+        :rtype: LabelTensor or torch.Tensor
         """
 
         # forward pass
@@ -356,7 +370,7 @@ 
    Source code for pina.model.deeponet
     
     DeepONet is a general architecture for learning Operators. Unlike
     traditional machine learning methods DeepONet is designed to map
-    entire functions to other functions. It can be trained both with 
+    entire functions to other functions. It can be trained both with
     Physics Informed or Supervised learning strategies.
 
     .. seealso::
@@ -369,15 +383,17 @@ 
    Source code for pina.model.deeponet
     
     """
 
-    def __init__(self,
-                 branch_net,
-                 trunk_net,
-                 input_indeces_branch_net,
-                 input_indeces_trunk_net,
-                 aggregator="*",
-                 reduction="+",
-                 scale=True,
-                 translation=True):
+    def __init__(
+        self,
+        branch_net,
+        trunk_net,
+        input_indeces_branch_net,
+        input_indeces_trunk_net,
+        aggregator="*",
+        reduction="+",
+        scale=True,
+        translation=True,
+    ):
         """
         :param torch.nn.Module branch_net: The neural network to use as branch
             model. It has to take as input a :py:obj:`pina.label_tensor.LabelTensor`
@@ -452,14 +468,15 @@ 
    Source code for pina.model.deeponet
             """
         networks = {
             branch_net: input_indeces_branch_net,
-            trunk_net: input_indeces_trunk_net
+            trunk_net: input_indeces_trunk_net,
         }
-        super().__init__(networks=networks,
-                         aggregator=aggregator,
-                         reduction=reduction,
-                         scale=scale,
-                         translation=translation)
-        
+        super().__init__(
+            networks=networks,
+            aggregator=aggregator,
+            reduction=reduction,
+            scale=scale,
+            translation=translation,
+        )
 
 
    [docs]    def forward(self, x):
         """
@@ -467,11 +484,10 @@ 
    Source code for pina.model.deeponet
     
         :param LabelTensor or torch.Tensor x: The input tensor for the forward call.
         :return: The output computed by the DeepONet model.
-        :rtype: LabelTensor or torch.Tensor 
+        :rtype: LabelTensor or torch.Tensor
         """
         return super().forward(x)
    
 
-
     @property
     def branch_net(self):
         """
@@ -494,8 +510,8 @@ 
    Source code for pina.model.deeponet
       
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/model/feed_forward.html b/_modules/pina/model/feed_forward.html
index 05d5e00c..a9d2a9fa 100644
--- a/_modules/pina/model/feed_forward.html
+++ b/_modules/pina/model/feed_forward.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.model.feed_forward — PINA 0.1 documentation
+  pina.model.feed_forward — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -88,6 +90,7 @@
              
   
    Source code for pina.model.feed_forward
     """Module for FeedForward model"""
+
 import torch
 import torch.nn as nn
 from ..utils import check_consistency
@@ -118,24 +121,25 @@ 
    Source code for pina.model.feed_forward
         :param bool bias: If ``True`` the MLP will consider some bias.
     """
 
-    def __init__(self,
-                 input_dimensions,
-                 output_dimensions,
-                 inner_size=20,
-                 n_layers=2,
-                 func=nn.Tanh,
-                 layers=None,
-                 bias=True):
-        """
-        """
+    def __init__(
+        self,
+        input_dimensions,
+        output_dimensions,
+        inner_size=20,
+        n_layers=2,
+        func=nn.Tanh,
+        layers=None,
+        bias=True,
+    ):
+        """ """
         super().__init__()
 
         if not isinstance(input_dimensions, int):
-            raise ValueError('input_dimensions expected to be int.')
+            raise ValueError("input_dimensions expected to be int.")
         self.input_dimension = input_dimensions
 
         if not isinstance(output_dimensions, int):
-            raise ValueError('output_dimensions expected to be int.')
+            raise ValueError("output_dimensions expected to be int.")
         self.output_dimension = output_dimensions
         if layers is None:
             layers = [inner_size] * n_layers
@@ -147,7 +151,8 @@ 
    Source code for pina.model.feed_forward
             self.layers = []
         for i in range(len(tmp_layers) - 1):
             self.layers.append(
-                nn.Linear(tmp_layers[i], tmp_layers[i + 1], bias=bias))
+                nn.Linear(tmp_layers[i], tmp_layers[i + 1], bias=bias)
+            )
 
         if isinstance(func, list):
             self.functions = func
@@ -155,7 +160,7 @@ 
    Source code for pina.model.feed_forward
                 self.functions = [func for _ in range(len(self.layers) - 1)]
 
         if len(self.layers) != len(self.functions) + 1:
-            raise RuntimeError('uncosistent number of layers and functions')
+            raise RuntimeError("uncosistent number of layers and functions")
 
         unique_list = []
         for layer, func in zip(self.layers[:-1], self.functions):
@@ -186,7 +191,7 @@ 
    Source code for pina.model.feed_forward
     
     .. seealso::
 
-        **Original reference**: Wang, Sifan, Yujun Teng, and Paris Perdikaris. 
+        **Original reference**: Wang, Sifan, Yujun Teng, and Paris Perdikaris.
         *Understanding and mitigating gradient flow pathologies in physics-informed
         neural networks*. SIAM Journal on Scientific Computing 43.5 (2021): A3055-A3081.
         DOI: `10.1137/20M1318043
@@ -213,16 +218,17 @@ 
    Source code for pina.model.feed_forward
             dimension must be the same as ``inner_size``.
     """
 
-    def __init__(self,
-                 input_dimensions,
-                 output_dimensions,
-                 inner_size=20,
-                 n_layers=2,
-                 func=nn.Tanh,
-                 bias=True,
-                 transformer_nets=None):
-        """
-        """
+    def __init__(
+        self,
+        input_dimensions,
+        output_dimensions,
+        inner_size=20,
+        n_layers=2,
+        func=nn.Tanh,
+        bias=True,
+        transformer_nets=None,
+    ):
+        """ """
         super().__init__()
 
         # check type consistency
@@ -237,35 +243,42 @@ 
    Source code for pina.model.feed_forward
             if transformer_nets is None:
             transformer_nets = [
                 EnhancedLinear(
-                    nn.Linear(in_features=input_dimensions,
-                              out_features=inner_size), nn.Tanh()),
+                    nn.Linear(
+                        in_features=input_dimensions, out_features=inner_size
+                    ),
+                    nn.Tanh(),
+                ),
                 EnhancedLinear(
-                    nn.Linear(in_features=input_dimensions,
-                              out_features=inner_size), nn.Tanh())
+                    nn.Linear(
+                        in_features=input_dimensions, out_features=inner_size
+                    ),
+                    nn.Tanh(),
+                ),
             ]
         elif isinstance(transformer_nets, (list, tuple)):
             if len(transformer_nets) != 2:
                 raise ValueError(
-                    'transformer_nets needs to be a list of len two.')
+                    "transformer_nets needs to be a list of len two."
+                )
             for net in transformer_nets:
                 if not isinstance(net, nn.Module):
                     raise ValueError(
-                        'transformer_nets needs to be a list of torch.nn.Module.'
+                        "transformer_nets needs to be a list of torch.nn.Module."
                     )
                 x = torch.rand(10, input_dimensions)
                 try:
                     out = net(x)
                 except RuntimeError:
                     raise ValueError(
-                        'transformer network input incompatible with input_dimensions.'
+                        "transformer network input incompatible with input_dimensions."
                     )
                 if out.shape[-1] != inner_size:
                     raise ValueError(
-                        'transformer network output incompatible with inner_size.'
+                        "transformer network output incompatible with inner_size."
                     )
         else:
             RuntimeError(
-                'Runtime error for transformer nets, check official documentation.'
+                "Runtime error for transformer nets, check official documentation."
             )
 
         # assign variables
@@ -282,10 +295,11 @@ 
    Source code for pina.model.feed_forward
             self.layers = []
         for i in range(len(tmp_layers) - 1):
             self.layers.append(
-                nn.Linear(tmp_layers[i], tmp_layers[i + 1], bias=bias))
-        self.last_layer = nn.Linear(tmp_layers[len(tmp_layers) - 1],
-                                    output_dimensions,
-                                    bias=bias)
+                nn.Linear(tmp_layers[i], tmp_layers[i + 1], bias=bias)
+            )
+        self.last_layer = nn.Linear(
+            tmp_layers[len(tmp_layers) - 1], output_dimensions, bias=bias
+        )
 
         if isinstance(func, list):
             self.functions = func()
@@ -293,7 +307,7 @@ 
    Source code for pina.model.feed_forward
                 self.functions = [func() for _ in range(len(self.layers))]
 
         if len(self.layers) != len(self.functions):
-            raise RuntimeError('uncosistent number of layers and functions')
+            raise RuntimeError("uncosistent number of layers and functions")
 
         unique_list = []
         for layer, func in zip(self.layers, self.functions):
@@ -317,7 +331,7 @@ 
    Source code for pina.model.feed_forward
             # skip connections pass
         for layer in self.inner_layers.children():
             x = layer(x)
-            x = (1. - x) * input_[0] + x * input_[1]
+            x = (1.0 - x) * input_[0] + x * input_[1]
 
         # last layer
         return self.last_layer(x)
    
@@ -330,8 +344,8 @@ 
    Source code for pina.model.feed_forward
       
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/model/fno.html b/_modules/pina/model/fno.html
index 739294cf..7ec538ef 100644
--- a/_modules/pina/model/fno.html
+++ b/_modules/pina/model/fno.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.model.fno — PINA 0.1 documentation
+  pina.model.fno — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -87,69 +89,84 @@
            
    
              
   
    Source code for pina.model.fno
    -import torch
+"""
+Fourier Neural Operator Module.
+"""
+
+import torch
 import torch.nn as nn
-from ..utils import check_consistency
-from .layers.fourier import FourierBlock1D, FourierBlock2D, FourierBlock3D
 from pina import LabelTensor
 import warnings
+from ..utils import check_consistency
+from .layers.fourier import FourierBlock1D, FourierBlock2D, FourierBlock3D
+from .base_no import KernelNeuralOperator
 
 
-
    [docs]class FNO(torch.nn.Module):
+
    [docs]class FourierIntegralKernel(torch.nn.Module):
     """
-    The PINA implementation of Fourier Neural Operator network.
+    Implementation of Fourier Integral Kernel network.
 
-    Fourier Neural Operator (FNO) is a general architecture for learning Operators.
-    Unlike traditional machine learning methods FNO is designed to map
-    entire functions to other functions. It can be trained both with 
-    Supervised learning strategies. FNO does global convolution by performing the
-    operation on the Fourier space.
+    This class implements the Fourier Integral Kernel network, which is a
+    PINA implementation of Fourier Neural Operator kernel network.
+    It performs global convolution by operating in the Fourier space.
 
     .. seealso::
 
-        **Original reference**: Li, Z., Kovachki, N., Azizzadenesheli, K., Liu, B.,
-        Bhattacharya, K., Stuart, A., & Anandkumar, A. (2020). *Fourier neural operator for
-        parametric partial differential equations*.
+        **Original reference**: Li, Z., Kovachki, N., Azizzadenesheli,
+        K., Liu, B., Bhattacharya, K., Stuart, A., & Anandkumar, A.
+        (2020). *Fourier neural operator for parametric partial
+        differential equations*.
         DOI: `arXiv preprint arXiv:2010.08895.
         <https://arxiv.org/abs/2010.08895>`_
     """
 
-    def __init__(self,
-                 lifting_net,
-                 projecting_net,
-                 n_modes,
-                 dimensions=3,
-                 padding=8,
-                 padding_type="constant",
-                 inner_size=20,
-                 n_layers=2,
-                 func=nn.Tanh,
-                 layers=None):
+    def __init__(
+        self,
+        input_numb_fields,
+        output_numb_fields,
+        n_modes,
+        dimensions=3,
+        padding=8,
+        padding_type="constant",
+        inner_size=20,
+        n_layers=2,
+        func=nn.Tanh,
+        layers=None,
+    ):
+        """
+        :param int input_numb_fields: Number of input fields.
+        :param int output_numb_fields: Number of output fields.
+        :param int | list[int] n_modes: Number of modes.
+        :param int dimensions: Number of dimensions (1, 2, or 3).
+        :param int padding: Padding size, defaults to 8.
+        :param str padding_type: Type of padding, defaults to "constant".
+        :param int inner_size: Inner size, defaults to 20.
+        :param int n_layers: Number of layers, defaults to 2.
+        :param torch.nn.Module func: Activation function, defaults to nn.Tanh.
+        :param list[int] layers: List of layer sizes, defaults to None.
+        """
         super().__init__()
 
         # check type consistency
-        check_consistency(lifting_net, nn.Module)
-        check_consistency(projecting_net, nn.Module)
         check_consistency(dimensions, int)
         check_consistency(padding, int)
         check_consistency(padding_type, str)
         check_consistency(inner_size, int)
         check_consistency(n_layers, int)
         check_consistency(func, nn.Module, subclass=True)
+
         if layers is not None:
             if isinstance(layers, (tuple, list)):
                 check_consistency(layers, int)
             else:
-                raise ValueError('layers must be tuple or list of int.')
+                raise ValueError("layers must be tuple or list of int.")
         if not isinstance(n_modes, (list, tuple, int)):
             raise ValueError(
-                'n_modes must be a int or list or tuple of valid modes.'
-                ' More information on the official documentation.')
+                "n_modes must be a int or list or tuple of valid modes."
+                " More information on the official documentation."
+            )
 
-        # assign variables
-        # TODO check input lifting net and input projecting net
-        self._lifting_net = lifting_net
-        self._projecting_net = projecting_net
+        # assign padding
         self._padding = padding
 
         # initialize fourier layer for each dimension
@@ -160,9 +177,9 @@ 
    Source code for pina.model.fno
             elif dimensions == 3:
             fourier_layer = FourierBlock3D
         else:
-            raise NotImplementedError('FNO implemented only for 1D/2D/3D data.')
+            raise NotImplementedError("FNO implemented only for 1D/2D/3D data.")
 
-        # Here we build the FNO by stacking Fourier Blocks
+        # Here we build the FNO kernels by stacking Fourier Blocks
 
         # 1. Assign output dimensions for each FNO layer
         if layers is None:
@@ -172,37 +189,39 @@ 
    Source code for pina.model.fno
             if isinstance(func, list):
             if len(layers) != len(func):
                 raise RuntimeError(
-                    'Uncosistent number of layers and functions.')
-            self._functions = func
+                    "Uncosistent number of layers and functions."
+                )
+            _functions = func
         else:
-            self._functions = [func for _ in range(len(layers))]
+            _functions = [func for _ in range(len(layers) - 1)]
+        _functions.append(torch.nn.Identity)
 
         # 3. Assign modes functions for each FNO layer
         if isinstance(n_modes, list):
-            if all(isinstance(i, list)
-                   for i in n_modes) and len(layers) != len(n_modes):
+            if all(isinstance(i, list) for i in n_modes) and len(layers) != len(
+                n_modes
+            ):
                 raise RuntimeError(
-                    'Uncosistent number of layers and functions.')
+                    "Uncosistent number of layers and functions."
+                )
             elif all(isinstance(i, int) for i in n_modes):
                 n_modes = [n_modes] * len(layers)
         else:
             n_modes = [n_modes] * len(layers)
 
         # 4. Build the FNO network
-        tmp_layers = layers.copy()
-        first_parameter = next(lifting_net.parameters())
-        input_shape = first_parameter.size()
-        out_feats = lifting_net(torch.rand(size=input_shape)).shape[-1]
-        tmp_layers.insert(0, out_feats)
-
-        self._layers = []
-        for i in range(len(tmp_layers) - 1):
-            self._layers.append(
-                fourier_layer(input_numb_fields=tmp_layers[i],
-                              output_numb_fields=tmp_layers[i + 1],
-                              n_modes=n_modes[i],
-                              activation=self._functions[i]))
-        self._layers = nn.Sequential(*self._layers)
+        _layers = []
+        tmp_layers = [input_numb_fields] + layers + [output_numb_fields]
+        for i in range(len(layers)):
+            _layers.append(
+                fourier_layer(
+                    input_numb_fields=tmp_layers[i],
+                    output_numb_fields=tmp_layers[i + 1],
+                    n_modes=n_modes[i],
+                    activation=_functions[i],
+                )
+            )
+        self._layers = nn.Sequential(*_layers)
 
         # 5. Padding values for spectral conv
         if isinstance(padding, int):
@@ -213,28 +232,29 @@ 
    Source code for pina.model.fno
                 val for pair in zip([0] * dimensions, padding) for val in pair
         ]
 
-
    [docs]    def forward(self, x):
+
    [docs]    def forward(self, x):
         """
         Forward computation for Fourier Neural Operator. It performs a
         lifting of the input by the ``lifting_net``. Then different layers
         of Fourier Blocks are applied. Finally the output is projected
         to the final dimensionality by the ``projecting_net``.
 
-        :param torch.Tensor x: The input tensor for fourier block, depending on
-            ``dimension`` in the initialization. In particular it is expected
+        :param torch.Tensor x: The input tensor for fourier block,
+            depending on ``dimension`` in the initialization.
+            In particular it is expected:
+
             * 1D tensors: ``[batch, X, channels]``
             * 2D tensors: ``[batch, X, Y, channels]``
             * 3D tensors: ``[batch, X, Y, Z, channels]``
-        :return: The output tensor obtained from the FNO.
+        :return: The output tensor obtained from the kernels convolution.
         :rtype: torch.Tensor
         """
-        if isinstance(x, LabelTensor): #TODO remove when Network is fixed
-            warnings.warn('LabelTensor passed as input is not allowed, casting LabelTensor to Torch.Tensor')
+        if isinstance(x, LabelTensor):  # TODO remove when Network is fixed
+            warnings.warn(
+                "LabelTensor passed as input is not allowed,"
+                " casting LabelTensor to Torch.Tensor"
+            )
             x = x.as_subclass(torch.Tensor)
-
-        # lifting the input in higher dimensional space
-        x = self._lifting_net(x)
-
         # permuting the input [batch, channels, x, y, ...]
         permutation_idx = [0, x.ndim - 1, *[i for i in range(1, x.ndim - 1)]]
         x = x.permute(permutation_idx)
@@ -253,8 +273,94 @@ 
    Source code for pina.model.fno
             permutation_idx = [0, *[i for i in range(2, x.ndim)], 1]
         x = x.permute(permutation_idx)
 
-        # apply projecting operator and return
-        return self._projecting_net(x)
    
+        return x
    
+
+
+
    [docs]class FNO(KernelNeuralOperator):
+    """
+    The PINA implementation of Fourier Neural Operator network.
+
+    Fourier Neural Operator (FNO) is a general architecture for
+    learning Operators. Unlike traditional machine learning methods
+    FNO is designed to map entire functions to other functions. It
+    can be trained with Supervised learning strategies. FNO does global
+    convolution by performing the operation on the Fourier space.
+
+    .. seealso::
+
+        **Original reference**: Li, Z., Kovachki, N., Azizzadenesheli,
+        K., Liu, B., Bhattacharya, K., Stuart, A., & Anandkumar, A.
+        (2020). *Fourier neural operator for parametric partial
+        differential equations*.
+        DOI: `arXiv preprint arXiv:2010.08895.
+        <https://arxiv.org/abs/2010.08895>`_
+    """
+
+    def __init__(
+        self,
+        lifting_net,
+        projecting_net,
+        n_modes,
+        dimensions=3,
+        padding=8,
+        padding_type="constant",
+        inner_size=20,
+        n_layers=2,
+        func=nn.Tanh,
+        layers=None,
+    ):
+        """
+        :param torch.nn.Module lifting_net: The neural network for lifting
+            the input.
+        :param torch.nn.Module projecting_net: The neural network for
+            projecting the output.
+        :param int | list[int] n_modes: Number of modes.
+        :param int dimensions: Number of dimensions (1, 2, or 3).
+        :param int padding: Padding size, defaults to 8.
+        :param str padding_type: Type of padding, defaults to `constant`.
+        :param int inner_size: Inner size, defaults to 20.
+        :param int n_layers: Number of layers, defaults to 2.
+        :param torch.nn.Module func: Activation function, defaults to nn.Tanh.
+        :param list[int] layers: List of layer sizes, defaults to None.
+        """
+        lifting_operator_out = lifting_net(
+            torch.rand(size=next(lifting_net.parameters()).size())
+        ).shape[-1]
+        super().__init__(
+            lifting_operator=lifting_net,
+            projection_operator=projecting_net,
+            integral_kernels=FourierIntegralKernel(
+                input_numb_fields=lifting_operator_out,
+                output_numb_fields=next(projecting_net.parameters()).size(),
+                n_modes=n_modes,
+                dimensions=dimensions,
+                padding=padding,
+                padding_type=padding_type,
+                inner_size=inner_size,
+                n_layers=n_layers,
+                func=func,
+                layers=layers,
+            ),
+        )
+
+
    [docs]    def forward(self, x):
+        """
+        Forward computation for Fourier Neural Operator. It performs a
+        lifting of the input by the ``lifting_net``. Then different layers
+        of Fourier Blocks are applied. Finally the output is projected
+        to the final dimensionality by the ``projecting_net``.
+
+        :param torch.Tensor x: The input tensor for fourier block,
+            depending on ``dimension`` in the initialization. In
+            particular it is expected:
+
+            * 1D tensors: ``[batch, X, channels]``
+            * 2D tensors: ``[batch, X, Y, channels]``
+            * 3D tensors: ``[batch, X, Y, Z, channels]``
+        :return: The output tensor obtained from FNO.
+        :rtype: torch.Tensor
+        """
+        return super().forward(x)
    
 
    
 
            
    
@@ -264,8 +370,8 @@ 
    Source code for pina.model.fno
       
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/model/layers/convolution_2d.html b/_modules/pina/model/layers/convolution_2d.html
index 67963eae..6bdb95d0 100644
--- a/_modules/pina/model/layers/convolution_2d.html
+++ b/_modules/pina/model/layers/convolution_2d.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.model.layers.convolution_2d — PINA 0.1 documentation
+  pina.model.layers.convolution_2d — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -88,6 +90,7 @@
              
   
    Source code for pina.model.layers.convolution_2d
     """Module for Continuous Convolution class"""
+
 from .convolution import BaseContinuousConv
 from .utils_convolution import check_point, map_points_
 from .integral import Integral
@@ -120,14 +123,16 @@ 
    Source code for pina.model.layers.convolution_2d
    
 
     """
 
-    def __init__(self,
-                 input_numb_field,
-                 output_numb_field,
-                 filter_dim,
-                 stride,
-                 model=None,
-                 optimize=False,
-                 no_overlap=False):
+    def __init__(
+        self,
+        input_numb_field,
+        output_numb_field,
+        filter_dim,
+        stride,
+        model=None,
+        optimize=False,
+        no_overlap=False,
+    ):
         """
         :param input_numb_field: Number of fields :math:`N_{in}` in the input.
         :type input_numb_field: int
@@ -201,16 +206,18 @@ 
    Source code for pina.model.layers.convolution_2d
    
                 )
         """
 
-        super().__init__(input_numb_field=input_numb_field,
-                         output_numb_field=output_numb_field,
-                         filter_dim=filter_dim,
-                         stride=stride,
-                         model=model,
-                         optimize=optimize,
-                         no_overlap=no_overlap)
+        super().__init__(
+            input_numb_field=input_numb_field,
+            output_numb_field=output_numb_field,
+            filter_dim=filter_dim,
+            stride=stride,
+            model=model,
+            optimize=optimize,
+            no_overlap=no_overlap,
+        )
 
         # integral routine
-        self._integral = Integral('discrete')
+        self._integral = Integral("discrete")
 
         # create the network
         self._net = self._spawn_networks(model)
@@ -235,15 +242,18 @@ 
    Source code for pina.model.layers.convolution_2d
    
                 nets.append(tmp)
         else:
             if not isinstance(model, object):
-                raise ValueError("Expected a python class inheriting"
-                                 " from torch.nn.Module")
+                raise ValueError(
+                    "Expected a python class inheriting" " from torch.nn.Module"
+                )
 
             for _ in range(self._input_numb_field * self._output_numb_field):
                 tmp = model()
                 if not isinstance(tmp, torch.nn.Module):
-                    raise ValueError("The python class must be inherited from"
-                                     " torch.nn.Module. See the docstring for"
-                                     " an example.")
+                    raise ValueError(
+                        "The python class must be inherited from"
+                        " torch.nn.Module. See the docstring for"
+                        " an example."
+                    )
                 nets.append(tmp)
 
         return torch.nn.ModuleList(nets)
@@ -321,11 +331,17 @@ 
    Source code for pina.model.layers.convolution_2d
    
         number_points = len(self._stride)
 
         # initialize the grid
-        grid = torch.zeros(size=(X.shape[0], self._output_numb_field,
-                                 number_points, filter_dim + 1),
-                           device=X.device,
-                           dtype=X.dtype)
-        grid[..., :-1] = (self._stride + self._dim * 0.5)
+        grid = torch.zeros(
+            size=(
+                X.shape[0],
+                self._output_numb_field,
+                number_points,
+                filter_dim + 1,
+            ),
+            device=X.device,
+            dtype=X.dtype,
+        )
+        grid[..., :-1] = self._stride + self._dim * 0.5
 
         # saving the grid
         self._grid = grid.detach()
@@ -358,14 +374,14 @@ 
    Source code for pina.model.layers.convolution_2d
    
 
         """
         # choose the type of convolution
-        if type == 'forward':
+        if type == "forward":
             return self._make_grid_forward(X)
-        elif type == 'inverse':
+        elif type == "inverse":
             self._make_grid_transpose(X)
         else:
             raise TypeError
 
-    def _initialize_convolution(self, X, type='forward'):
+    def _initialize_convolution(self, X, type="forward"):
         """
         Private method to intialize the convolution.
         The convolution is initialized by setting a grid and
@@ -396,10 +412,10 @@ 
    Source code for pina.model.layers.convolution_2d
    
 
         # initialize convolution
         if self.training:  # we choose what to do based on optimization
-            self._choose_initialization(X, type='forward')
+            self._choose_initialization(X, type="forward")
 
         else:  # we always initialize on testing
-            self._initialize_convolution(X, 'forward')
+            self._initialize_convolution(X, "forward")
 
         # create convolutional array
         conv = self._grid.clone().detach()
@@ -411,7 +427,8 @@ 
    Source code for pina.model.layers.convolution_2d
    
 
             # extract mapped points
             stacked_input, indeces_channels = self._extract_mapped_points(
-                batch_idx, self._index, x)
+                batch_idx, self._index, x
+            )
 
             # compute the convolution
 
@@ -428,9 +445,11 @@ 
    Source code for pina.model.layers.convolution_2d
    
                 # calculate filter value
                 staked_output = net(single_channel_input[..., :-1])
                 # perform integral for all strides in one field
-                integral = self._integral(staked_output,
-                                          single_channel_input[..., -1],
-                                          indeces_channels[idx])
+                integral = self._integral(
+                    staked_output,
+                    single_channel_input[..., -1],
+                    indeces_channels[idx],
+                )
                 res_tmp.append(integral)
 
             # stacking integral results
@@ -438,9 +457,9 @@ 
    Source code for pina.model.layers.convolution_2d
    
 
             # sum filters (for each input fields) in groups
             # for different ouput fields
-            conv[batch_idx, ...,
-                 -1] = res_tmp.reshape(self._output_numb_field,
-                                       self._input_numb_field, -1).sum(1)
+            conv[batch_idx, ..., -1] = res_tmp.reshape(
+                self._output_numb_field, self._input_numb_field, -1
+            ).sum(1)
         return conv
    
 
 
    [docs]    def transpose_no_overlap(self, integrals, X):
@@ -471,10 +490,10 @@ 
    Source code for pina.model.layers.convolution_2d
    
 
         # initialize convolution
         if self.training:  # we choose what to do based on optimization
-            self._choose_initialization(X, type='inverse')
+            self._choose_initialization(X, type="inverse")
 
         else:  # we always initialize on testing
-            self._initialize_convolution(X, 'inverse')
+            self._initialize_convolution(X, "inverse")
 
         # initialize grid
         X = self._grid_transpose.clone().detach()
@@ -487,7 +506,8 @@ 
    Source code for pina.model.layers.convolution_2d
    
 
             # extract mapped points
             stacked_input, indeces_channels = self._extract_mapped_points(
-                batch_idx, self._index, x)
+                batch_idx, self._index, x
+            )
 
             # compute the transpose convolution
 
@@ -503,8 +523,9 @@ 
    Source code for pina.model.layers.convolution_2d
    
                 # extract input for each field
                 single_channel_input = stacked_input[idx]
                 rep_idx = torch.tensor(indeces_channels[idx])
-                integral = integrals[batch_idx,
-                                     idx_in, :].repeat_interleave(rep_idx)
+                integral = integrals[batch_idx, idx_in, :].repeat_interleave(
+                    rep_idx
+                )
                 # extract filter
                 net = self._net[idx_conv]
                 # perform transpose convolution for all strides in one field
@@ -515,9 +536,11 @@ 
    Source code for pina.model.layers.convolution_2d
    
             # stacking integral results and sum
             # filters (for each input fields) in groups
             # for different output fields
-            res_tmp = torch.stack(res_tmp).reshape(self._input_numb_field,
-                                                   self._output_numb_field,
-                                                   -1).sum(0)
+            res_tmp = (
+                torch.stack(res_tmp)
+                .reshape(self._input_numb_field, self._output_numb_field, -1)
+                .sum(0)
+            )
             conv_transposed[batch_idx, ..., -1] = res_tmp
 
         return conv_transposed
    
@@ -549,10 +572,10 @@ 
    Source code for pina.model.layers.convolution_2d
    
 
         # initialize convolution
         if self.training:  # we choose what to do based on optimization
-            self._choose_initialization(X, type='inverse')
+            self._choose_initialization(X, type="inverse")
 
         else:  # we always initialize on testing
-            self._initialize_convolution(X, 'inverse')
+            self._initialize_convolution(X, "inverse")
 
         # initialize grid
         X = self._grid_transpose.clone().detach()
@@ -568,11 +591,14 @@ 
    Source code for pina.model.layers.convolution_2d
    
 
             # accumulator for the convolution on different batches
             accumulator_batch = torch.zeros(
-                size=(self._grid_transpose.shape[1],
-                      self._grid_transpose.shape[2]),
+                size=(
+                    self._grid_transpose.shape[1],
+                    self._grid_transpose.shape[2],
+                ),
                 requires_grad=True,
                 device=X.device,
-                dtype=X.dtype).clone()
+                dtype=X.dtype,
+            ).clone()
 
             for stride_idx, current_stride in enumerate(self._stride):
                 # indeces of points falling into filter range
@@ -611,9 +637,10 @@ 
    Source code for pina.model.layers.convolution_2d
    
                     staked_output = net(nn_input_pts[idx_channel_out])
 
                     # perform integral for all strides in one field
-                    integral = staked_output * integrals[batch_idx,
-                                                         idx_channel_in,
-                                                         stride_idx]
+                    integral = (
+                        staked_output
+                        * integrals[batch_idx, idx_channel_in, stride_idx]
+                    )
                     # append results
                     res_tmp.append(integral.flatten())
 
@@ -621,7 +648,7 @@ 
    Source code for pina.model.layers.convolution_2d
    
                 channel_sum = []
                 start = 0
                 for _ in range(self._output_numb_field):
-                    tmp = res_tmp[start:start + self._input_numb_field]
+                    tmp = res_tmp[start : start + self._input_numb_field]
                     tmp = torch.vstack(tmp).sum(dim=0)
                     channel_sum.append(tmp)
                     start += self._input_numb_field
@@ -642,8 +669,8 @@ 
    Source code for pina.model.layers.convolution_2d
    
   
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/model/layers/fourier.html b/_modules/pina/model/layers/fourier.html
index f15258ea..c15edc9e 100644
--- a/_modules/pina/model/layers/fourier.html
+++ b/_modules/pina/model/layers/fourier.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.model.layers.fourier — PINA 0.1 documentation
+  pina.model.layers.fourier — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -91,14 +93,18 @@ 
    Source code for pina.model.layers.fourier
     import torch.nn as nn
 from ...utils import check_consistency
 
-from pina.model.layers import SpectralConvBlock1D, SpectralConvBlock2D, SpectralConvBlock3D
+from pina.model.layers import (
+    SpectralConvBlock1D,
+    SpectralConvBlock2D,
+    SpectralConvBlock3D,
+)
 
 
 
    [docs]class FourierBlock1D(nn.Module):
     """
     Fourier block implementation for three dimensional
     input tensor. The combination of Fourier blocks
-    make up the Fourier Neural Operator  
+    make up the Fourier Neural Operator
 
     .. seealso::
 
@@ -110,11 +116,13 @@ 
    Source code for pina.model.layers.fourier
     
     """
 
-    def __init__(self,
-                 input_numb_fields,
-                 output_numb_fields,
-                 n_modes,
-                 activation=torch.nn.Tanh):
+    def __init__(
+        self,
+        input_numb_fields,
+        output_numb_fields,
+        n_modes,
+        activation=torch.nn.Tanh,
+    ):
         super().__init__()
         """
         PINA implementation of Fourier block one dimension. The module computes
@@ -140,17 +148,18 @@ 
    Source code for pina.model.layers.fourier
             self._spectral_conv = SpectralConvBlock1D(
             input_numb_fields=input_numb_fields,
             output_numb_fields=output_numb_fields,
-            n_modes=n_modes)
+            n_modes=n_modes,
+        )
         self._activation = activation()
         self._linear = nn.Conv1d(input_numb_fields, output_numb_fields, 1)
 
 
    [docs]    def forward(self, x):
         """
-        Forward computation for Fourier Block. It performs a spectral 
+        Forward computation for Fourier Block. It performs a spectral
         convolution and a linear transformation of the input and sum the
         results.
 
-        :param x: The input tensor for fourier block, expect of size 
+        :param x: The input tensor for fourier block, expect of size
             ``[batch, input_numb_fields, x]``.
         :type x: torch.Tensor
         :return: The output tensor obtained from the
@@ -164,7 +173,7 @@ 
    Source code for pina.model.layers.fourier
         """
     Fourier block implementation for two dimensional
     input tensor. The combination of Fourier blocks
-    make up the Fourier Neural Operator    
+    make up the Fourier Neural Operator
 
     .. seealso::
 
@@ -176,18 +185,20 @@ 
    Source code for pina.model.layers.fourier
     
     """
 
-    def __init__(self,
-                 input_numb_fields,
-                 output_numb_fields,
-                 n_modes,
-                 activation=torch.nn.Tanh):
+    def __init__(
+        self,
+        input_numb_fields,
+        output_numb_fields,
+        n_modes,
+        activation=torch.nn.Tanh,
+    ):
         """
         PINA implementation of Fourier block two dimensions. The module computes
         the spectral convolution of the input with a linear kernel in the
         fourier space, and then it maps the input back to the physical
         space. The output is then added to a Linear tranformation of the
         input in the physical space. Finally an activation function is
-        applied to the output. 
+        applied to the output.
 
         The block expects an input of size ``[batch, input_numb_fields, Nx, Ny]``
         and returns an output of size ``[batch, output_numb_fields, Nx, Ny]``.
@@ -207,17 +218,18 @@ 
    Source code for pina.model.layers.fourier
             self._spectral_conv = SpectralConvBlock2D(
             input_numb_fields=input_numb_fields,
             output_numb_fields=output_numb_fields,
-            n_modes=n_modes)
+            n_modes=n_modes,
+        )
         self._activation = activation()
         self._linear = nn.Conv2d(input_numb_fields, output_numb_fields, 1)
 
 
    [docs]    def forward(self, x):
         """
-        Forward computation for Fourier Block. It performs a spectral 
+        Forward computation for Fourier Block. It performs a spectral
         convolution and a linear transformation of the input and sum the
         results.
 
-        :param x: The input tensor for fourier block, expect of size 
+        :param x: The input tensor for fourier block, expect of size
             ``[batch, input_numb_fields, x, y]``.
         :type x: torch.Tensor
         :return: The output tensor obtained from the
@@ -231,7 +243,7 @@ 
    Source code for pina.model.layers.fourier
         """
     Fourier block implementation for three dimensional
     input tensor. The combination of Fourier blocks
-    make up the Fourier Neural Operator  
+    make up the Fourier Neural Operator
 
     .. seealso::
 
@@ -243,18 +255,20 @@ 
    Source code for pina.model.layers.fourier
     
     """
 
-    def __init__(self,
-                 input_numb_fields,
-                 output_numb_fields,
-                 n_modes,
-                 activation=torch.nn.Tanh):
+    def __init__(
+        self,
+        input_numb_fields,
+        output_numb_fields,
+        n_modes,
+        activation=torch.nn.Tanh,
+    ):
         """
         PINA implementation of Fourier block three dimensions. The module computes
         the spectral convolution of the input with a linear kernel in the
         fourier space, and then it maps the input back to the physical
         space. The output is then added to a Linear tranformation of the
         input in the physical space. Finally an activation function is
-        applied to the output. 
+        applied to the output.
 
         The block expects an input of size ``[batch, input_numb_fields, Nx, Ny, Nz]``
         and returns an output of size ``[batch, output_numb_fields, Nx, Ny, Nz]``.
@@ -275,17 +289,18 @@ 
    Source code for pina.model.layers.fourier
             self._spectral_conv = SpectralConvBlock3D(
             input_numb_fields=input_numb_fields,
             output_numb_fields=output_numb_fields,
-            n_modes=n_modes)
+            n_modes=n_modes,
+        )
         self._activation = activation()
         self._linear = nn.Conv3d(input_numb_fields, output_numb_fields, 1)
 
 
    [docs]    def forward(self, x):
         """
-        Forward computation for Fourier Block. It performs a spectral 
+        Forward computation for Fourier Block. It performs a spectral
         convolution and a linear transformation of the input and sum the
         results.
 
-        :param x: The input tensor for fourier block, expect of size 
+        :param x: The input tensor for fourier block, expect of size
             ``[batch, input_numb_fields, x, y, z]``.
         :type x: torch.Tensor
         :return: The output tensor obtained from the
@@ -302,8 +317,8 @@ 
    Source code for pina.model.layers.fourier
       
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/model/layers/residual.html b/_modules/pina/model/layers/residual.html
index 95dc9c84..c9980bf2 100644
--- a/_modules/pina/model/layers/residual.html
+++ b/_modules/pina/model/layers/residual.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.model.layers.residual — PINA 0.1 documentation
+  pina.model.layers.residual — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -105,18 +107,20 @@ 
    Source code for pina.model.layers.residual
     
     """
 
-    def __init__(self,
-                 input_dim,
-                 output_dim,
-                 hidden_dim,
-                 spectral_norm=False,
-                 activation=torch.nn.ReLU()):
+    def __init__(
+        self,
+        input_dim,
+        output_dim,
+        hidden_dim,
+        spectral_norm=False,
+        activation=torch.nn.ReLU(),
+    ):
         """
         Initializes the ResidualBlock module.
 
         :param int input_dim: Dimension of the input to pass to the
             feedforward linear layer.
-        :param int output_dim: Dimension of the output from the 
+        :param int output_dim: Dimension of the output from the
             residual layer.
         :param int hidden_dim: Hidden dimension for mapping the input
             (first block).
@@ -171,6 +175,7 @@ 
    Source code for pina.model.layers.residual
     import torch
 import torch.nn as nn
 
+
 
    [docs]class EnhancedLinear(torch.nn.Module):
     """
     A wrapper class for enhancing a linear layer with activation and/or dropout.
@@ -221,8 +226,9 @@ 
    Source code for pina.model.layers.residual
                 self._model = torch.nn.Sequential(layer, self._drop(dropout))
 
         elif (dropout is not None) and (activation is not None):
-            self._model = torch.nn.Sequential(layer, activation,
-                                              self._drop(dropout))
+            self._model = torch.nn.Sequential(
+                layer, activation, self._drop(dropout)
+            )
 
 
    [docs]    def forward(self, x):
         """
@@ -256,8 +262,8 @@ 
    Source code for pina.model.layers.residual
       
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/model/layers/spectral.html b/_modules/pina/model/layers/spectral.html
index a129ff7a..ff8f01d4 100644
--- a/_modules/pina/model/layers/spectral.html
+++ b/_modules/pina/model/layers/spectral.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.model.layers.spectral — PINA 0.1 documentation
+  pina.model.layers.spectral — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -126,18 +128,23 @@ 
    Source code for pina.model.layers.spectral
             self._output_channels = output_numb_fields
 
         # scaling factor
-        scale = (1. / (self._input_channels * self._output_channels))
-        self._weights = nn.Parameter(scale * torch.rand(self._input_channels,
-                                                        self._output_channels,
-                                                        self._modes,
-                                                        dtype=torch.cfloat))
+        scale = 1.0 / (self._input_channels * self._output_channels)
+        self._weights = nn.Parameter(
+            scale
+            * torch.rand(
+                self._input_channels,
+                self._output_channels,
+                self._modes,
+                dtype=torch.cfloat,
+            )
+        )
 
     def _compute_mult1d(self, input, weights):
         """
         Compute the matrix multiplication of the input
         with the linear kernel weights.
 
-        :param input: The input tensor, expect of size 
+        :param input: The input tensor, expect of size
             ``[batch, input_numb_fields, x]``.
         :type input: torch.Tensor
         :param weights: The kernel weights, expect of
@@ -153,7 +160,7 @@ 
    Source code for pina.model.layers.spectral
             """
         Forward computation for Spectral Convolution.
 
-        :param x: The input tensor, expect of size 
+        :param x: The input tensor, expect of size
             ``[batch, input_numb_fields, x]``.
         :type x: torch.Tensor
         :return: The output tensor obtained from the
@@ -166,13 +173,16 @@ 
    Source code for pina.model.layers.spectral
             x_ft = torch.fft.rfft(x)
 
         # Multiply relevant Fourier modes
-        out_ft = torch.zeros(batch_size,
-                             self._output_channels,
-                             x.size(-1) // 2 + 1,
-                             device=x.device,
-                             dtype=torch.cfloat)
-        out_ft[:, :, :self._modes] = self._compute_mult1d(
-            x_ft[:, :, :self._modes], self._weights)
+        out_ft = torch.zeros(
+            batch_size,
+            self._output_channels,
+            x.size(-1) // 2 + 1,
+            device=x.device,
+            dtype=torch.cfloat,
+        )
+        out_ft[:, :, : self._modes] = self._compute_mult1d(
+            x_ft[:, :, : self._modes], self._weights
+        )
 
         # Return to physical space
         return torch.fft.irfft(out_ft, n=x.size(-1))
    
@@ -208,17 +218,19 @@ 
    Source code for pina.model.layers.spectral
             if isinstance(n_modes, (tuple, list)):
             if len(n_modes) != 2:
                 raise ValueError(
-                    'Expected n_modes to be a list or tuple of len two, '
-                    'with each entry corresponding to the number of modes '
-                    'for each dimension ')
+                    "Expected n_modes to be a list or tuple of len two, "
+                    "with each entry corresponding to the number of modes "
+                    "for each dimension "
+                )
         elif isinstance(n_modes, int):
             n_modes = [n_modes] * 2
         else:
             raise ValueError(
-                'Expected n_modes to be a list or tuple of len two, '
-                'with each entry corresponding to the number of modes '
-                'for each dimension; or an int value representing the '
-                'number of modes for all dimensions')
+                "Expected n_modes to be a list or tuple of len two, "
+                "with each entry corresponding to the number of modes "
+                "for each dimension; or an int value representing the "
+                "number of modes for all dimensions"
+            )
 
         # assign variables
         self._modes = n_modes
@@ -226,24 +238,34 @@ 
    Source code for pina.model.layers.spectral
             self._output_channels = output_numb_fields
 
         # scaling factor
-        scale = (1. / (self._input_channels * self._output_channels))
-        self._weights1 = nn.Parameter(scale * torch.rand(self._input_channels,
-                                                         self._output_channels,
-                                                         self._modes[0],
-                                                         self._modes[1],
-                                                         dtype=torch.cfloat))
-        self._weights2 = nn.Parameter(scale * torch.rand(self._input_channels,
-                                                         self._output_channels,
-                                                         self._modes[0],
-                                                         self._modes[1],
-                                                         dtype=torch.cfloat))
+        scale = 1.0 / (self._input_channels * self._output_channels)
+        self._weights1 = nn.Parameter(
+            scale
+            * torch.rand(
+                self._input_channels,
+                self._output_channels,
+                self._modes[0],
+                self._modes[1],
+                dtype=torch.cfloat,
+            )
+        )
+        self._weights2 = nn.Parameter(
+            scale
+            * torch.rand(
+                self._input_channels,
+                self._output_channels,
+                self._modes[0],
+                self._modes[1],
+                dtype=torch.cfloat,
+            )
+        )
 
     def _compute_mult2d(self, input, weights):
         """
         Compute the matrix multiplication of the input
         with the linear kernel weights.
 
-        :param input: The input tensor, expect of size 
+        :param input: The input tensor, expect of size
             ``[batch, input_numb_fields, x, y]``.
         :type input: torch.Tensor
         :param weights: The kernel weights, expect of
@@ -259,7 +281,7 @@ 
    Source code for pina.model.layers.spectral
             """
         Forward computation for Spectral Convolution.
 
-        :param x: The input tensor, expect of size 
+        :param x: The input tensor, expect of size
             ``[batch, input_numb_fields, x, y]``.
         :type x: torch.Tensor
         :return: The output tensor obtained from the
@@ -273,16 +295,22 @@ 
    Source code for pina.model.layers.spectral
             x_ft = torch.fft.rfft2(x)
 
         # Multiply relevant Fourier modes
-        out_ft = torch.zeros(batch_size,
-                             self._output_channels,
-                             x.size(-2),
-                             x.size(-1) // 2 + 1,
-                             device=x.device,
-                             dtype=torch.cfloat)
-        out_ft[:, :, :self._modes[0], :self._modes[1]] = self._compute_mult2d(
-            x_ft[:, :, :self._modes[0], :self._modes[1]], self._weights1)
-        out_ft[:, :, -self._modes[0]:, :self._modes[1]:] = self._compute_mult2d(
-            x_ft[:, :, -self._modes[0]:, :self._modes[1]], self._weights2)
+        out_ft = torch.zeros(
+            batch_size,
+            self._output_channels,
+            x.size(-2),
+            x.size(-1) // 2 + 1,
+            device=x.device,
+            dtype=torch.cfloat,
+        )
+        out_ft[:, :, : self._modes[0], : self._modes[1]] = self._compute_mult2d(
+            x_ft[:, :, : self._modes[0], : self._modes[1]], self._weights1
+        )
+        out_ft[:, :, -self._modes[0] :, : self._modes[1] :] = (
+            self._compute_mult2d(
+                x_ft[:, :, -self._modes[0] :, : self._modes[1]], self._weights2
+            )
+        )
 
         # Return to physical space
         return torch.fft.irfft2(out_ft, s=(x.size(-2), x.size(-1)))
    
@@ -319,17 +347,19 @@ 
    Source code for pina.model.layers.spectral
             if isinstance(n_modes, (tuple, list)):
             if len(n_modes) != 3:
                 raise ValueError(
-                    'Expected n_modes to be a list or tuple of len three, '
-                    'with each entry corresponding to the number of modes '
-                    'for each dimension ')
+                    "Expected n_modes to be a list or tuple of len three, "
+                    "with each entry corresponding to the number of modes "
+                    "for each dimension "
+                )
         elif isinstance(n_modes, int):
             n_modes = [n_modes] * 3
         else:
             raise ValueError(
-                'Expected n_modes to be a list or tuple of len three, '
-                'with each entry corresponding to the number of modes '
-                'for each dimension; or an int value representing the '
-                'number of modes for all dimensions')
+                "Expected n_modes to be a list or tuple of len three, "
+                "with each entry corresponding to the number of modes "
+                "for each dimension; or an int value representing the "
+                "number of modes for all dimensions"
+            )
 
         # assign variables
         self._modes = n_modes
@@ -337,38 +367,58 @@ 
    Source code for pina.model.layers.spectral
             self._output_channels = output_numb_fields
 
         # scaling factor
-        scale = (1. / (self._input_channels * self._output_channels))
-        self._weights1 = nn.Parameter(scale * torch.rand(self._input_channels,
-                                                         self._output_channels,
-                                                         self._modes[0],
-                                                         self._modes[1],
-                                                         self._modes[2],
-                                                         dtype=torch.cfloat))
-        self._weights2 = nn.Parameter(scale * torch.rand(self._input_channels,
-                                                         self._output_channels,
-                                                         self._modes[0],
-                                                         self._modes[1],
-                                                         self._modes[2],
-                                                         dtype=torch.cfloat))
-        self._weights3 = nn.Parameter(scale * torch.rand(self._input_channels,
-                                                         self._output_channels,
-                                                         self._modes[0],
-                                                         self._modes[1],
-                                                         self._modes[2],
-                                                         dtype=torch.cfloat))
-        self._weights4 = nn.Parameter(scale * torch.rand(self._input_channels,
-                                                         self._output_channels,
-                                                         self._modes[0],
-                                                         self._modes[1],
-                                                         self._modes[2],
-                                                         dtype=torch.cfloat))
+        scale = 1.0 / (self._input_channels * self._output_channels)
+        self._weights1 = nn.Parameter(
+            scale
+            * torch.rand(
+                self._input_channels,
+                self._output_channels,
+                self._modes[0],
+                self._modes[1],
+                self._modes[2],
+                dtype=torch.cfloat,
+            )
+        )
+        self._weights2 = nn.Parameter(
+            scale
+            * torch.rand(
+                self._input_channels,
+                self._output_channels,
+                self._modes[0],
+                self._modes[1],
+                self._modes[2],
+                dtype=torch.cfloat,
+            )
+        )
+        self._weights3 = nn.Parameter(
+            scale
+            * torch.rand(
+                self._input_channels,
+                self._output_channels,
+                self._modes[0],
+                self._modes[1],
+                self._modes[2],
+                dtype=torch.cfloat,
+            )
+        )
+        self._weights4 = nn.Parameter(
+            scale
+            * torch.rand(
+                self._input_channels,
+                self._output_channels,
+                self._modes[0],
+                self._modes[1],
+                self._modes[2],
+                dtype=torch.cfloat,
+            )
+        )
 
     def _compute_mult3d(self, input, weights):
         """
         Compute the matrix multiplication of the input
         with the linear kernel weights.
 
-        :param input: The input tensor, expect of size 
+        :param input: The input tensor, expect of size
             ``[batch, input_numb_fields, x, y, z]``.
         :type input: torch.Tensor
         :param weights: The kernel weights, expect of
@@ -384,7 +434,7 @@ 
    Source code for pina.model.layers.spectral
             """
         Forward computation for Spectral Convolution.
 
-        :param x: The input tensor, expect of size 
+        :param x: The input tensor, expect of size
             ``[batch, input_numb_fields, x, y, z]``.
         :type x: torch.Tensor
         :return: The output tensor obtained from the
@@ -398,13 +448,15 @@ 
    Source code for pina.model.layers.spectral
             x_ft = torch.fft.rfftn(x, dim=[-3, -2, -1])
 
         # Multiply relevant Fourier modes
-        out_ft = torch.zeros(batch_size,
-                             self._output_channels,
-                             x.size(-3),
-                             x.size(-2),
-                             x.size(-1) // 2 + 1,
-                             device=x.device,
-                             dtype=torch.cfloat)
+        out_ft = torch.zeros(
+            batch_size,
+            self._output_channels,
+            x.size(-3),
+            x.size(-2),
+            x.size(-1) // 2 + 1,
+            device=x.device,
+            dtype=torch.cfloat,
+        )
 
         slice0 = (
             slice(None),
@@ -453,8 +505,8 @@ 
    Source code for pina.model.layers.spectral
       
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/model/multi_feed_forward.html b/_modules/pina/model/multi_feed_forward.html
index 9b4a1a7e..268ce891 100644
--- a/_modules/pina/model/multi_feed_forward.html
+++ b/_modules/pina/model/multi_feed_forward.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.model.multi_feed_forward — PINA 0.1 documentation
+  pina.model.multi_feed_forward — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -88,6 +90,7 @@
              
   
    Source code for pina.model.multi_feed_forward
     """Module for Multi FeedForward model"""
+
 import torch
 
 from .feed_forward import FeedForward
@@ -95,7 +98,7 @@ 
    Source code for pina.model.multi_feed_forward
    [docs]class MultiFeedForward(torch.nn.Module):
     """
-    The PINA implementation of MultiFeedForward network. 
+    The PINA implementation of MultiFeedForward network.
 
     This model allows to create a network with multiple FeedForward combined
     together. The user has to define the `forward` method choosing how to
@@ -121,8 +124,8 @@ 
    Source code for pina.model.multi_feed_forward
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/model/network.html b/_modules/pina/model/network.html
index f983b6f6..e1faa69d 100644
--- a/_modules/pina/model/network.html
+++ b/_modules/pina/model/network.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.model.network — PINA 0.1 documentation
+  pina.model.network — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -95,13 +97,15 @@ 
    Source code for pina.model.network
     
 
    [docs]class Network(torch.nn.Module):
 
-    def __init__(self, model, input_variables, output_variables, extra_features=None):
+    def __init__(
+        self, model, input_variables, output_variables, extra_features=None
+    ):
         """
         Network class with standard forward method
         and possibility to pass extra features. This
         class is used internally in PINA to convert
         any :class:`torch.nn.Module` s in a PINA module.
-    
+
         :param model: The torch model to convert in a PINA model.
         :type model: torch.nn.Module
         :param list(str) input_variables: The input variables of the :class:`AbstractProblem`, whose type depends on the
@@ -146,7 +150,9 @@ 
    Source code for pina.model.network
             :return torch.Tensor: Output of the network.
         """
         # only labeltensors as input
-        assert isinstance(x, LabelTensor), "Expected LabelTensor as input to the model."
+        assert isinstance(
+            x, LabelTensor
+        ), "Expected LabelTensor as input to the model."
 
         # extract torch.Tensor from corresponding label
         # in case `input_variables = []` all points are used
@@ -164,7 +170,7 @@ 
    Source code for pina.model.network
             output.labels = self._output_variables
 
         return output
    
-    
+
     # TODO to remove in next releases (only used in GAROM solver)
 
    [docs]    def forward_map(self, x):
         """
@@ -209,8 +215,8 @@ 
    Source code for pina.model.network
       
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/operators.html b/_modules/pina/operators.html
index 49b90130..814a5e1f 100644
--- a/_modules/pina/operators.html
+++ b/_modules/pina/operators.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.operators — PINA 0.1 documentation
+  pina.operators — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -94,6 +96,7 @@ 
    Source code for pina.operators
     to which computing the operator, the name of the output variables to calculate the operator
 for (in case of multidimensional functions), and the variables name on which the operator is calculated.
 """
+
 import torch
 
 from pina.label_tensor import LabelTensor
@@ -138,24 +141,25 @@ 
    Source code for pina.operators
             """
 
         if len(output_.labels) != 1:
-            raise RuntimeError('only scalar function can be differentiated')
+            raise RuntimeError("only scalar function can be differentiated")
         if not all([di in input_.labels for di in d]):
-            raise RuntimeError('derivative labels missing from input tensor')
+            raise RuntimeError("derivative labels missing from input tensor")
 
         output_fieldname = output_.labels[0]
-        gradients = torch.autograd.grad(output_,
-                                        input_,
-                                        grad_outputs=torch.ones(
-                                            output_.size(),
-                                            dtype=output_.dtype,
-                                            device=output_.device),
-                                        create_graph=True,
-                                        retain_graph=True,
-                                        allow_unused=True)[0]
+        gradients = torch.autograd.grad(
+            output_,
+            input_,
+            grad_outputs=torch.ones(
+                output_.size(), dtype=output_.dtype, device=output_.device
+            ),
+            create_graph=True,
+            retain_graph=True,
+            allow_unused=True,
+        )[0]
 
         gradients.labels = input_.labels
         gradients = gradients.extract(d)
-        gradients.labels = [f'd{output_fieldname}d{i}' for i in d]
+        gradients.labels = [f"d{output_fieldname}d{i}" for i in d]
 
         return gradients
 
@@ -182,7 +186,8 @@ 
    Source code for pina.operators
                     gradients = grad_scalar_output(c_output, input_, d)
             else:
                 gradients = gradients.append(
-                    grad_scalar_output(c_output, input_, d))
+                    grad_scalar_output(c_output, input_, d)
+                )
     else:
         raise NotImplementedError
 
@@ -222,7 +227,7 @@ 
    Source code for pina.operators
             components = output_.labels
 
     if output_.shape[1] < 2 or len(components) < 2:
-        raise ValueError('div supported only for vector fields')
+        raise ValueError("div supported only for vector fields")
 
     if len(components) != len(d):
         raise ValueError
@@ -231,16 +236,16 @@ 
    Source code for pina.operators
         div = torch.zeros(input_.shape[0], 1, device=output_.device)
     labels = [None] * len(components)
     for i, (c, d) in enumerate(zip(components, d)):
-        c_fields = f'd{c}d{d}'
+        c_fields = f"d{c}d{d}"
         div[:, 0] += grad_output.extract(c_fields).sum(axis=1)
         labels[i] = c_fields
 
     div = div.as_subclass(LabelTensor)
-    div.labels = ['+'.join(labels)]
+    div.labels = ["+".join(labels)]
     return div
    
 
 
-
    [docs]def laplacian(output_, input_, components=None, d=None, method='std'):
+
    [docs]def laplacian(output_, input_, components=None, d=None, method="std"):
     """
     Compute Laplace operator. The operator works for vectorial and
     scalar functions, with multiple input coordinates.
@@ -271,26 +276,27 @@ 
    Source code for pina.operators
         if len(components) != len(d) and len(components) != 1:
         raise ValueError
 
-    if method == 'divgrad':
-        raise NotImplementedError('divgrad not implemented as method')
+    if method == "divgrad":
+        raise NotImplementedError("divgrad not implemented as method")
         # TODO fix
         # grad_output = grad(output_, input_, components, d)
         # result = div(grad_output, input_, d=d)
-    elif method == 'std':
+    elif method == "std":
 
         if len(components) == 1:
             grad_output = grad(output_, input_, components=components, d=d)
             result = torch.zeros(output_.shape[0], 1, device=output_.device)
             for i, label in enumerate(grad_output.labels):
                 gg = grad(grad_output, input_, d=d, components=[label])
-                result[:, 0] += super(torch.Tensor,
-                                      gg.T).__getitem__(i)  # TODO improve
-            labels = [f'dd{components[0]}']
+                result[:, 0] += super(torch.Tensor, gg.T).__getitem__(
+                    i
+                )  # TODO improve
+            labels = [f"dd{components[0]}"]
 
         else:
-            result = torch.empty(input_.shape[0],
-                                 len(components),
-                                 device=output_.device)
+            result = torch.empty(
+                input_.shape[0], len(components), device=output_.device
+            )
             labels = [None] * len(components)
             for idx, (ci, di) in enumerate(zip(components, d)):
 
@@ -301,7 +307,7 @@ 
    Source code for pina.operators
     
                 grad_output = grad(output_, input_, components=ci, d=di)
                 result[:, idx] = grad(grad_output, input_, d=di).flatten()
-                labels[idx] = f'dd{ci}dd{di}'
+                labels[idx] = f"dd{ci}dd{di}"
 
     result = result.as_subclass(LabelTensor)
     result.labels = labels
@@ -334,8 +340,11 @@ 
    Source code for pina.operators
         if components is None:
         components = output_.labels
 
-    tmp = grad(output_, input_, components, d).reshape(-1, len(components),
-                                                       len(d)).transpose(0, 1)
+    tmp = (
+        grad(output_, input_, components, d)
+        .reshape(-1, len(components), len(d))
+        .transpose(0, 1)
+    )
 
     tmp *= output_.extract(velocity_field)
     return tmp.sum(dim=2).T
    
@@ -348,8 +357,8 @@ 
    Source code for pina.operators
       
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/plotter.html b/_modules/pina/plotter.html
index 2d546b51..c4ff6f0b 100644
--- a/_modules/pina/plotter.html
+++ b/_modules/pina/plotter.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.plotter — PINA 0.1 documentation
+  pina.plotter — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -100,14 +102,17 @@ 
    Source code for pina.plotter
         Implementation of a plotter class, for easy visualizations.
     """
 
-
    [docs]    def plot_samples(self, problem, variables=None, **kwargs):
+
    [docs]    def plot_samples(self, problem, variables=None, filename=None, **kwargs):
         """
         Plot the training grid samples.
 
-        :param SolverInterface solver: The ``SolverInterface`` object.
+        :param AbstractProblem problem: The PINA problem from where to plot
+            the domain.
         :param list(str) variables: Variables to plot. If None, all variables
             are plotted. If 'spatial', only spatial variables are plotted. If
             'temporal', only temporal variables are plotted. Defaults to None.
+        :param str filename: The file name to save the plot. If None, the plot
+            is shown using the setted matplotlib frontend. Default is None.
 
         .. todo::
             - Add support for 3D plots.
@@ -120,49 +125,61 @@ 
    Source code for pina.plotter
     
         if variables is None:
             variables = problem.domain.variables
-        elif variables == 'spatial':
+        elif variables == "spatial":
             variables = problem.spatial_domain.variables
-        elif variables == 'temporal':
+        elif variables == "temporal":
             variables = problem.temporal_domain.variables
 
         if len(variables) not in [1, 2, 3]:
-            raise ValueError
+            raise ValueError(
+                "Samples can be plotted only in " "dimensions 1, 2 and 3."
+            )
 
         fig = plt.figure()
-        proj = '3d' if len(variables) == 3 else None
+        proj = "3d" if len(variables) == 3 else None
         ax = fig.add_subplot(projection=proj)
         for location in problem.input_pts:
             coords = problem.input_pts[location].extract(variables).T.detach()
-            if coords.shape[0] == 1:  # 1D samples
-                ax.plot(coords.flatten(),
-                        torch.zeros(coords.flatten().shape),
-                        '.',
-                        label=location,
-                        **kwargs)
-            else:
-                ax.plot(*coords, '.', label=location, **kwargs)
+            if len(variables) == 1:  # 1D samples
+                ax.plot(
+                    coords.flatten(),
+                    torch.zeros(coords.flatten().shape),
+                    ".",
+                    label=location,
+                    **kwargs,
+                )
+            elif len(variables) == 2:
+                ax.plot(*coords, ".", label=location, **kwargs)
+            elif len(variables) == 3:
+                ax.scatter(*coords, ".", label=location, **kwargs)
 
         ax.set_xlabel(variables[0])
         try:
             ax.set_ylabel(variables[1])
-        except:
+        except (IndexError, AttributeError):
             pass
 
         try:
             ax.set_zlabel(variables[2])
-        except:
+        except (IndexError, AttributeError):
             pass
 
         plt.legend()
-        plt.show()
    
+        if filename:
+            plt.savefig(filename)
+            plt.close()
+        else:
+            plt.show()
    
 
-    def _1d_plot(self, pts, pred, method, truth_solution=None, **kwargs):
+    def _1d_plot(self, pts, pred, v, method, truth_solution=None, **kwargs):
         """Plot solution for one dimensional function
 
         :param pts: Points to plot the solution.
         :type pts: torch.Tensor
         :param pred: SolverInterface solution evaluated at 'pts'.
         :type pred: torch.Tensor
+        :param v: Fixed variables when plotting the solution.
+        :type v: torch.Tensor
         :param method: Not used, kept for code compatibility
         :type method: None
         :param truth_solution: Real solution evaluated at 'pts',
@@ -171,33 +188,31 @@ 
    Source code for pina.plotter
             """
         fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(8, 8))
 
-        ax.plot(pts, pred.detach(), label='Neural Network solution', **kwargs)
+        ax.plot(pts.extract(v), pred, label="Neural Network solution", **kwargs)
 
         if truth_solution:
-            truth_output = truth_solution(pts).float()
-            ax.plot(pts, truth_output.detach(), label='True solution', **kwargs)
+            truth_output = truth_solution(pts).detach()
+            ax.plot(
+                pts.extract(v), truth_output, label="True solution", **kwargs
+            )
 
         # TODO: pred is a torch.Tensor, so no labels is available
         #      extra variable for labels should be
         #      passed in the function arguments.
-        # plt.ylabel(pred.labels[0]) 
+        # plt.ylabel(pred.labels[0])
         plt.legend()
-        plt.show()
-
-    def _2d_plot(self,
-                 pts,
-                 pred,
-                 v,
-                 res,
-                 method,
-                 truth_solution=None,
-                 **kwargs):
+
+    def _2d_plot(
+        self, pts, pred, v, res, method, truth_solution=None, **kwargs
+    ):
         """Plot solution for two dimensional function
 
         :param pts: Points to plot the solution.
         :type pts: torch.Tensor
         :param pred: ``SolverInterface`` solution evaluated at 'pts'.
         :type pred: torch.Tensor
+        :param v: Fixed variables when plotting the solution.
+        :type v: torch.Tensor
         :param method: Matplotlib method to plot 2-dimensional data,
             see https://matplotlib.org/stable/api/axes_api.html for
             reference.
@@ -207,48 +222,52 @@ 
    Source code for pina.plotter
             :type truth_solution: torch.Tensor, optional
         """
 
-        grids = [p_.reshape(res, res) for p_ in pts.extract(v).cpu().T]
+        grids = [p_.reshape(res, res) for p_ in pts.extract(v).T]
 
         pred_output = pred.reshape(res, res)
         if truth_solution:
-            truth_output = truth_solution(pts).float().reshape(res, res).as_subclass(torch.Tensor)
+            truth_output = (
+                truth_solution(pts)
+                .float()
+                .reshape(res, res)
+                .as_subclass(torch.Tensor)
+            )
             fig, ax = plt.subplots(nrows=1, ncols=3, figsize=(16, 6))
 
-            cb = getattr(ax[0], method)(*grids, pred_output.cpu().detach(),
-                                        **kwargs)
+            cb = getattr(ax[0], method)(*grids, pred_output, **kwargs)
             fig.colorbar(cb, ax=ax[0])
-            ax[0].title.set_text('Neural Network prediction')
-            cb = getattr(ax[1], method)(*grids, truth_output.cpu().detach(),
-                                        **kwargs)
+            ax[0].title.set_text("Neural Network prediction")
+            cb = getattr(ax[1], method)(*grids, truth_output, **kwargs)
             fig.colorbar(cb, ax=ax[1])
-            ax[1].title.set_text('True solution')
-            cb = getattr(ax[2],
-                         method)(*grids,
-                                 (truth_output - pred_output).cpu().detach(),
-                                 **kwargs)
+            ax[1].title.set_text("True solution")
+            cb = getattr(ax[2], method)(
+                *grids, (truth_output - pred_output), **kwargs
+            )
             fig.colorbar(cb, ax=ax[2])
-            ax[2].title.set_text('Residual')
+            ax[2].title.set_text("Residual")
         else:
             fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(8, 6))
-            cb = getattr(ax, method)(*grids, pred_output.cpu().detach(),
-                                     **kwargs)
+            cb = getattr(ax, method)(*grids, pred_output, **kwargs)
             fig.colorbar(cb, ax=ax)
-            ax.title.set_text('Neural Network prediction')
-
-
    [docs]    def plot(self,
-             solver,
-             components=None,
-             fixed_variables={},
-             method='contourf',
-             res=256,
-             filename=None,
-             **kwargs):
+            ax.title.set_text("Neural Network prediction")
+
+
    [docs]    def plot(
+        self,
+        solver,
+        components=None,
+        fixed_variables={},
+        method="contourf",
+        res=256,
+        filename=None,
+        **kwargs,
+    ):
         """
         Plot sample of SolverInterface output.
 
         :param SolverInterface solver: The ``SolverInterface`` object instance.
-        :param list(str) components: The output variable to plot. If None, all
-            the output variables of the problem are selected. Default value is None.
+        :param str | list(str) components: The output variable(s) to plot.
+            If None, all the output variables of the problem are selected.
+            Default value is None.
         :param dict fixed_variables: A dictionary with all the variables that
             should be kept fixed during the plot. The keys of the dictionary
             are the variables name whereas the values are the corresponding
@@ -264,15 +283,28 @@ 
    Source code for pina.plotter
     
         if components is None:
             components = solver.problem.output_variables
-        
+
+        if isinstance(components, str):
+            components = [components]
+
+        if not isinstance(components, list):
+            raise NotImplementedError(
+                "Output variables must be passed"
+                "as a string or a list of strings."
+            )
+
         if len(components) > 1:
-            raise NotImplementedError('Multidimensional plots are not implemented, '
-                                      'set components to an available components of the problem.')
+            raise NotImplementedError(
+                "Multidimensional plots are not implemented, "
+                "set components to an available components of"
+                " the problem."
+            )
         v = [
-            var for var in solver.problem.input_variables
+            var
+            for var in solver.problem.input_variables
             if var not in fixed_variables.keys()
         ]
-        pts = solver.problem.domain.sample(res, 'grid', variables=v)
+        pts = solver.problem.domain.sample(res, "grid", variables=v)
 
         fixed_pts = torch.ones(pts.shape[0], len(fixed_variables))
         fixed_pts *= torch.tensor(list(fixed_variables.values()))
@@ -282,29 +314,39 @@ 
    Source code for pina.plotter
             pts = pts.append(fixed_pts)
         pts = pts.to(device=solver.device)
 
-        predicted_output = solver.forward(pts).extract(components).as_subclass(torch.Tensor)
-        truth_solution = getattr(solver.problem, 'truth_solution', None)
+        # computing soluting and sending to cpu
+        predicted_output = solver.forward(pts).extract(components)
+        predicted_output = (
+            predicted_output.as_subclass(torch.Tensor).cpu().detach()
+        )
+        pts = pts.cpu()
+        truth_solution = getattr(solver.problem, "truth_solution", None)
 
         if len(v) == 1:
-            self._1d_plot(pts.extract(v), predicted_output, method, truth_solution,
-                          **kwargs)
+            self._1d_plot(
+                pts, predicted_output, v, method, truth_solution, **kwargs
+            )
         elif len(v) == 2:
-            self._2d_plot(pts, predicted_output, v, res, method, truth_solution,
-                          **kwargs)
+            self._2d_plot(
+                pts, predicted_output, v, res, method, truth_solution, **kwargs
+            )
 
         plt.tight_layout()
         if filename:
             plt.savefig(filename)
+            plt.close()
         else:
             plt.show()
    
 
-
    [docs]    def plot_loss(self,
-                  trainer,
-                  metrics=None,
-                  logy=False,
-                  logx=False,
-                  filename=None,
-                  **kwargs):
+
    [docs]    def plot_loss(
+        self,
+        trainer,
+        metrics=None,
+        logy=False,
+        logx=False,
+        filename=None,
+        **kwargs,
+    ):
         """
         Plot the loss function values during traininig.
 
@@ -322,45 +364,48 @@ 
    Source code for pina.plotter
     
         # check that MetricTracker has been used
         list_ = [
-            idx for idx, s in enumerate(trainer.callbacks)
+            idx
+            for idx, s in enumerate(trainer.callbacks)
             if isinstance(s, MetricTracker)
         ]
         if not bool(list_):
             raise FileNotFoundError(
-                'MetricTracker should be used as a callback during training to'
-                ' use this method.')
+                "MetricTracker should be used as a callback during training to"
+                " use this method."
+            )
 
         # extract trainer metrics
         trainer_metrics = trainer.callbacks[list_[0]].metrics
         if metrics is None:
-            metrics = ['mean_loss']
+            metrics = ["mean_loss"]
         elif not isinstance(metrics, list):
-            raise ValueError('metrics must be class list.')
+            raise ValueError("metrics must be class list.")
 
         # loop over metrics to plot
         for metric in metrics:
             if metric not in trainer_metrics:
                 raise ValueError(
-                    f'{metric} not a valid metric. Available metrics are {list(trainer_metrics.keys())}.'
+                    f"{metric} not a valid metric. Available metrics are {list(trainer_metrics.keys())}."
                 )
             loss = trainer_metrics[metric]
             epochs = range(len(loss))
-            plt.plot(epochs, loss, **kwargs)
+            plt.plot(epochs, loss.cpu(), **kwargs)
 
         # plotting
-        plt.xlabel('epoch')
-        plt.ylabel('loss')
+        plt.xlabel("epoch")
+        plt.ylabel("loss")
         plt.legend()
 
         # log axis
         if logy:
-            plt.yscale('log')
+            plt.yscale("log")
         if logx:
-            plt.xscale('log')
+            plt.xscale("log")
 
         # saving in file
         if filename:
-            plt.savefig(filename)
    
+            plt.savefig(filename)
+            plt.close()
    
 
    
 
            
    
@@ -370,8 +415,8 @@ 
    Source code for pina.plotter
       
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/problem/abstract_problem.html b/_modules/pina/problem/abstract_problem.html
index 557b270e..236bb7ff 100644
--- a/_modules/pina/problem/abstract_problem.html
+++ b/_modules/pina/problem/abstract_problem.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.problem.abstract_problem — PINA 0.1 documentation
+  pina.problem.abstract_problem — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -88,6 +90,7 @@
              
   
    Source code for pina.problem.abstract_problem
     """ Module for AbstractProblem class """
+
 from abc import ABCMeta, abstractmethod
 from ..utils import merge_tensors, check_consistency
 import torch
@@ -129,13 +132,13 @@ 
    Source code for pina.problem.abstract_problem
            """
         variables = []
 
-        if hasattr(self, 'spatial_variables'):
+        if hasattr(self, "spatial_variables"):
             variables += self.spatial_variables
-        if hasattr(self, 'temporal_variable'):
+        if hasattr(self, "temporal_variable"):
             variables += self.temporal_variable
-        if hasattr(self, 'parameters'):
+        if hasattr(self, "parameters"):
             variables += self.parameters
-        if hasattr(self, 'custom_variables'):
+        if hasattr(self, "custom_variables"):
             variables += self.custom_variables
 
         return variables
@@ -151,9 +154,9 @@ 
    Source code for pina.problem.abstract_problem
            :rtype: list[Location]
         """
         domains = [
-            getattr(self, f'{t}_domain')
-            for t in ['spatial', 'temporal', 'parameter']
-            if hasattr(self, f'{t}_domain')
+            getattr(self, f"{t}_domain")
+            for t in ["spatial", "temporal", "parameter"]
+            if hasattr(self, f"{t}_domain")
         ]
 
         if len(domains) == 1:
@@ -166,7 +169,7 @@ 
    Source code for pina.problem.abstract_problem
    [domain.update(d) for d in domains]
             return domain
         else:
-            raise RuntimeError('different domains')
+            raise RuntimeError("different domains")
 
     @input_variables.setter
     def input_variables(self, variables):
@@ -194,24 +197,27 @@ 
    Source code for pina.problem.abstract_problem
            """
         for condition_name in self.conditions:
             condition = self.conditions[condition_name]
-            if hasattr(condition, 'input_points'):
+            if hasattr(condition, "input_points"):
                 samples = condition.input_points
                 self.input_pts[condition_name] = samples
                 self._have_sampled_points[condition_name] = True
-            if hasattr(self, 'unknown_parameter_domain'):
+            if hasattr(self, "unknown_parameter_domain"):
                 # initialize the unknown parameters of the inverse problem given
                 # the domain the user gives
                 self.unknown_parameters = {}
                 for i, var in enumerate(self.unknown_variables):
                     range_var = self.unknown_parameter_domain.range_[var]
-                    tensor_var = torch.rand(1, requires_grad=True) * range_var[1] + range_var[0]
-                    self.unknown_parameters[var] = torch.nn.Parameter(tensor_var)
-
-
    [docs]    def discretise_domain(self,
-                          n,
-                          mode='random',
-                          variables='all',
-                          locations='all'):
+                    tensor_var = (
+                        torch.rand(1, requires_grad=True) * range_var[1]
+                        + range_var[0]
+                    )
+                    self.unknown_parameters[var] = torch.nn.Parameter(
+                        tensor_var
+                    )
+
+
    [docs]    def discretise_domain(
+        self, n, mode="random", variables="all", locations="all"
+    ):
         """
         Generate a set of points to span the `Location` of all the conditions of
         the problem.
@@ -246,28 +252,32 @@ 
    Source code for pina.problem.abstract_problem
    # check consistency mode
         check_consistency(mode, str)
-        if mode not in ['random', 'grid', 'lh', 'chebyshev', 'latin']:
-            raise TypeError(f'mode {mode} not valid.')
+        if mode not in ["random", "grid", "lh", "chebyshev", "latin"]:
+            raise TypeError(f"mode {mode} not valid.")
 
         # check consistency variables
-        if variables == 'all':
+        if variables == "all":
             variables = self.input_variables
         else:
             check_consistency(variables, str)
 
         if sorted(variables) != sorted(self.input_variables):
-            TypeError(f'Wrong variables for sampling. Variables ',
-                      f'should be in {self.input_variables}.')
+            TypeError(
+                f"Wrong variables for sampling. Variables ",
+                f"should be in {self.input_variables}.",
+            )
 
         # check consistency location
-        if locations == 'all':
+        if locations == "all":
             locations = [condition for condition in self.conditions]
         else:
             check_consistency(locations, str)
 
         if sorted(locations) != sorted(self.conditions):
-            TypeError(f'Wrong locations for sampling. Location ',
-                      f'should be in {self.conditions}.')
+            TypeError(
+                f"Wrong locations for sampling. Location ",
+                f"should be in {self.conditions}.",
+            )
 
         # sampling
         for location in locations:
@@ -297,10 +307,10 @@ 
    Source code for pina.problem.abstract_problem
    # the condition is sampled if input_pts contains all labels
             if sorted(self.input_pts[location].labels) == sorted(
-                    self.input_variables):
+                self.input_variables
+            ):
                 self._have_sampled_points[location] = True
    
 
-
 
    [docs]    def add_points(self, new_points):
         """
         Adding points to the already sampled points.
@@ -310,8 +320,10 @@ 
    Source code for pina.problem.abstract_problem
            """
 
         if sorted(new_points.keys()) != sorted(self.conditions):
-            TypeError(f'Wrong locations for new points. Location ',
-                      f'should be in {self.conditions}.')
+            TypeError(
+                f"Wrong locations for new points. Location ",
+                f"should be in {self.conditions}.",
+            )
 
         for location in new_points.keys():
             # extract old and new points
@@ -320,11 +332,14 @@ 
    Source code for pina.problem.abstract_problem
    # if they don't have the same variables error
             if sorted(old_pts.labels) != sorted(new_pts.labels):
-                TypeError(f'Not matching variables for old and new points '
-                          f'in condition {location}.')
+                TypeError(
+                    f"Not matching variables for old and new points "
+                    f"in condition {location}."
+                )
             if old_pts.labels != new_pts.labels:
                 new_pts = torch.hstack(
-                    [new_pts.extract([i]) for i in old_pts.labels])
+                    [new_pts.extract([i]) for i in old_pts.labels]
+                )
                 new_pts.labels = old_pts.labels
 
             # merging
@@ -355,7 +370,6 @@ 
    Source code for pina.problem.abstract_problem
    if not is_sample:
                     not_sampled.append(condition_name)
         return not_sampled
    
-
 
    
 
            
    
@@ -365,8 +379,8 @@ 
    Source code for pina.problem.abstract_problem
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/problem/parametric_problem.html b/_modules/pina/problem/parametric_problem.html
index 4f7ca0a0..706ec56a 100644
--- a/_modules/pina/problem/parametric_problem.html
+++ b/_modules/pina/problem/parametric_problem.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.problem.parametric_problem — PINA 0.1 documentation
+  pina.problem.parametric_problem — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -88,6 +90,7 @@
              
   
    Source code for pina.problem.parametric_problem
     """Module for the ParametricProblem class"""
+
 from abc import abstractmethod
 
 from .abstract_problem import AbstractProblem
@@ -150,8 +153,8 @@ 
    Source code for pina.problem.parametric_problem
    <
   
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/problem/spatial_problem.html b/_modules/pina/problem/spatial_problem.html
index 6968c26d..3f9359a2 100644
--- a/_modules/pina/problem/spatial_problem.html
+++ b/_modules/pina/problem/spatial_problem.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.problem.spatial_problem — PINA 0.1 documentation
+  pina.problem.spatial_problem — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -88,6 +90,7 @@
              
   
    Source code for pina.problem.spatial_problem
     """Module for the SpatialProblem class"""
+
 from abc import abstractmethod
 
 from .abstract_problem import AbstractProblem
@@ -146,8 +149,8 @@ 
    Source code for pina.problem.spatial_problem
     
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/problem/timedep_problem.html b/_modules/pina/problem/timedep_problem.html
index 8ad153e0..f3d6bddb 100644
--- a/_modules/pina/problem/timedep_problem.html
+++ b/_modules/pina/problem/timedep_problem.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.problem.timedep_problem — PINA 0.1 documentation
+  pina.problem.timedep_problem — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -88,6 +90,7 @@
              
   
    Source code for pina.problem.timedep_problem
     """Module for the TimeDependentProblem class"""
+
 from abc import abstractmethod
 
 from .abstract_problem import AbstractProblem
@@ -156,8 +159,8 @@ 
    Source code for pina.problem.timedep_problem
     
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/solvers/garom.html b/_modules/pina/solvers/garom.html
index 347ae3c9..74783244 100644
--- a/_modules/pina/solvers/garom.html
+++ b/_modules/pina/solvers/garom.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.solvers.garom — PINA 0.1 documentation
+  pina.solvers.garom — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -90,10 +92,14 @@ 
    Source code for pina.solvers.garom
     """ Module for GAROM """
 
 import torch
+import sys
+
 try:
     from torch.optim.lr_scheduler import LRScheduler  # torch >= 2.0
 except ImportError:
-    from torch.optim.lr_scheduler import _LRScheduler as LRScheduler  # torch < 2.0
+    from torch.optim.lr_scheduler import (
+        _LRScheduler as LRScheduler,
+    )  # torch < 2.0
 
 from torch.optim.lr_scheduler import ConstantLR
 from .solver import SolverInterface
@@ -106,12 +112,12 @@ 
    Source code for pina.solvers.garom
         """
     GAROM solver class. This class implements Generative Adversarial
     Reduced Order Model solver, using user specified ``models`` to solve
-    a specific order reduction``problem``. 
+    a specific order reduction``problem``.
 
     .. seealso::
 
         **Original reference**: Coscia, D., Demo, N., & Rozza, G. (2023).
-        *Generative Adversarial Reduced Order Modelling*. 
+        *Generative Adversarial Reduced Order Modelling*.
         DOI: `arXiv preprint arXiv:2305.15881.
         <https://doi.org/10.48550/arXiv.2305.15881>`_.
     """
@@ -123,19 +129,13 @@ 
    Source code for pina.solvers.garom
             discriminator,
         loss=None,
         optimizer_generator=torch.optim.Adam,
-        optimizer_generator_kwargs={'lr': 0.001},
+        optimizer_generator_kwargs={"lr": 0.001},
         optimizer_discriminator=torch.optim.Adam,
-        optimizer_discriminator_kwargs={'lr': 0.001},
+        optimizer_discriminator_kwargs={"lr": 0.001},
         scheduler_generator=ConstantLR,
-        scheduler_generator_kwargs={
-            "factor": 1,
-            "total_iters": 0
-        },
+        scheduler_generator_kwargs={"factor": 1, "total_iters": 0},
         scheduler_discriminator=ConstantLR,
-        scheduler_discriminator_kwargs={
-            "factor": 1,
-            "total_iters": 0
-        },
+        scheduler_discriminator_kwargs={"factor": 1, "total_iters": 0},
         gamma=0.3,
         lambda_k=0.001,
         regularizer=False,
@@ -183,8 +183,10 @@ 
    Source code for pina.solvers.garom
                 problem=problem,
             optimizers=[optimizer_generator, optimizer_discriminator],
             optimizers_kwargs=[
-                optimizer_generator_kwargs, optimizer_discriminator_kwargs
-            ])
+                optimizer_generator_kwargs,
+                optimizer_discriminator_kwargs,
+            ],
+        )
 
         # set automatic optimization for GANs
         self.automatic_optimization = False
@@ -206,13 +208,14 @@ 
    Source code for pina.solvers.garom
             # assign schedulers
         self._schedulers = [
             scheduler_generator(
-                self.optimizers[0], **scheduler_generator_kwargs),
+                self.optimizers[0], **scheduler_generator_kwargs
+            ),
             scheduler_discriminator(
-                self.optimizers[1],
-                **scheduler_discriminator_kwargs)
+                self.optimizers[1], **scheduler_discriminator_kwargs
+            ),
         ]
 
-        # loss and writer 
+        # loss and writer
         self._loss = loss
 
         # began hyperparameters
@@ -229,7 +232,7 @@ 
    Source code for pina.solvers.garom
     
         :param x: The input tensor.
         :type x: torch.Tensor
-        :param mc_steps: Number of montecarlo samples to approximate the 
+        :param mc_steps: Number of montecarlo samples to approximate the
             expected value, defaults to 20.
         :type mc_steps: int
         :param variance: Returining also the sample variance of the solution, defaults to False.
@@ -277,8 +280,12 @@ 
    Source code for pina.solvers.garom
     
         # generator loss
         r_loss = self._loss(snapshots, generated_snapshots)
-        d_fake = self.discriminator.forward_map([generated_snapshots, parameters])
-        g_loss = self._loss(d_fake, generated_snapshots) + self.regularizer * r_loss
+        d_fake = self.discriminator.forward_map(
+            [generated_snapshots, parameters]
+        )
+        g_loss = (
+            self._loss(d_fake, generated_snapshots) + self.regularizer * r_loss
+        )
 
         # backward step
         g_loss.backward()
@@ -298,7 +305,9 @@ 
    Source code for pina.solvers.garom
     
         # Discriminator pass
         d_real = self.discriminator.forward_map([snapshots, parameters])
-        d_fake = self.discriminator.forward_map([generated_snapshots, parameters]) 
+        d_fake = self.discriminator.forward_map(
+            [generated_snapshots, parameters]
+        )
 
         # evaluate loss
         d_loss_real = self._loss(d_real, snapshots)
@@ -323,7 +332,7 @@ 
    Source code for pina.solvers.garom
             self.k += self.lambda_k * diff.item()
         self.k = min(max(self.k, 0), 1)  # Constraint to interval [0, 1]
         return diff
-    
+
 
    [docs]    def training_step(self, batch, batch_idx):
         """GAROM solver training step.
 
@@ -336,38 +345,75 @@ 
    Source code for pina.solvers.garom
             """
 
         dataloader = self.trainer.train_dataloader
-        condition_idx = batch['condition']
+        condition_idx = batch["condition"]
 
-        for condition_id in range(condition_idx.min(), condition_idx.max()+1):
+        for condition_id in range(condition_idx.min(), condition_idx.max() + 1):
+
+            if sys.version_info >= (3, 8):
+                condition_name = dataloader.condition_names[condition_id]
+            else:
+                condition_name = dataloader.loaders.condition_names[
+                    condition_id
+                ]
 
-            condition_name = dataloader.condition_names[condition_id]
             condition = self.problem.conditions[condition_name]
-            pts = batch['pts'].detach()
-            out = batch['output']
+            pts = batch["pts"].detach()
+            out = batch["output"]
 
             if condition_name not in self.problem.conditions:
-                raise RuntimeError('Something wrong happened.')
+                raise RuntimeError("Something wrong happened.")
 
             # for data driven mode
-            if not hasattr(condition, 'output_points'):
-                raise NotImplementedError('GAROM works only in data-driven mode.')
+            if not hasattr(condition, "output_points"):
+                raise NotImplementedError(
+                    "GAROM works only in data-driven mode."
+                )
 
             # get data
             snapshots = out[condition_idx == condition_id]
             parameters = pts[condition_idx == condition_id]
 
             d_loss_real, d_loss_fake, d_loss = self._train_discriminator(
-                parameters, snapshots)
+                parameters, snapshots
+            )
 
             r_loss, g_loss = self._train_generator(parameters, snapshots)
-            
+
             diff = self._update_weights(d_loss_real, d_loss_fake)
 
             # logging
-            self.log('mean_loss', float(r_loss), prog_bar=True, logger=True, on_epoch=True, on_step=False)
-            self.log('d_loss', float(d_loss), prog_bar=True, logger=True, on_epoch=True, on_step=False)
-            self.log('g_loss', float(g_loss), prog_bar=True, logger=True, on_epoch=True, on_step=False)
-            self.log('stability_metric', float(d_loss_real + torch.abs(diff)), prog_bar=True, logger=True, on_epoch=True, on_step=False)
+            self.log(
+                "mean_loss",
+                float(r_loss),
+                prog_bar=True,
+                logger=True,
+                on_epoch=True,
+                on_step=False,
+            )
+            self.log(
+                "d_loss",
+                float(d_loss),
+                prog_bar=True,
+                logger=True,
+                on_epoch=True,
+                on_step=False,
+            )
+            self.log(
+                "g_loss",
+                float(g_loss),
+                prog_bar=True,
+                logger=True,
+                on_epoch=True,
+                on_step=False,
+            )
+            self.log(
+                "stability_metric",
+                float(d_loss_real + torch.abs(diff)),
+                prog_bar=True,
+                logger=True,
+                on_epoch=True,
+                on_step=False,
+            )
 
         return
    
 
@@ -403,8 +449,8 @@ 
    Source code for pina.solvers.garom
       
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/solvers/pinn.html b/_modules/pina/solvers/pinn.html
index f671bc11..525837c1 100644
--- a/_modules/pina/solvers/pinn.html
+++ b/_modules/pina/solvers/pinn.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.solvers.pinn — PINA 0.1 documentation
+  pina.solvers.pinn — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -88,12 +90,17 @@
              
   
    Source code for pina.solvers.pinn
     """ Module for PINN """
+
 import torch
+
 try:
     from torch.optim.lr_scheduler import LRScheduler  # torch >= 2.0
 except ImportError:
-    from torch.optim.lr_scheduler import _LRScheduler as LRScheduler  # torch < 2.0
+    from torch.optim.lr_scheduler import (
+        _LRScheduler as LRScheduler,
+    )  # torch < 2.0
 
+import sys
 from torch.optim.lr_scheduler import ConstantLR
 
 from .solver import SolverInterface
@@ -127,14 +134,11 @@ 
    Source code for pina.solvers.pinn
             extra_features=None,
         loss=torch.nn.MSELoss(),
         optimizer=torch.optim.Adam,
-        optimizer_kwargs={'lr': 0.001},
+        optimizer_kwargs={"lr": 0.001},
         scheduler=ConstantLR,
-        scheduler_kwargs={
-            "factor": 1,
-            "total_iters": 0
-        },
+        scheduler_kwargs={"factor": 1, "total_iters": 0},
     ):
-        '''
+        """
         :param AbstractProblem problem: The formulation of the problem.
         :param torch.nn.Module model: The neural network model to use.
         :param torch.nn.Module loss: The loss function used as minimizer,
@@ -147,12 +151,14 @@ 
    Source code for pina.solvers.pinn
             :param torch.optim.LRScheduler scheduler: Learning
             rate scheduler.
         :param dict scheduler_kwargs: LR scheduler constructor keyword args.
-        '''
-        super().__init__(models=[model],
-                         problem=problem,
-                         optimizers=[optimizer],
-                         optimizers_kwargs=[optimizer_kwargs],
-                         extra_features=extra_features)
+        """
+        super().__init__(
+            models=[model],
+            problem=problem,
+            optimizers=[optimizer],
+            optimizers_kwargs=[optimizer_kwargs],
+            extra_features=extra_features,
+        )
 
         # check consistency
         check_consistency(scheduler, LRScheduler, subclass=True)
@@ -193,15 +199,21 @@ 
    Source code for pina.solvers.pinn
             # to the parameters that the optimizer needs to optimize
         if isinstance(self.problem, InverseProblem):
             self.optimizers[0].add_param_group(
-                {'params': [self._params[var] for var in self.problem.unknown_variables]}
-                )
+                {
+                    "params": [
+                        self._params[var]
+                        for var in self.problem.unknown_variables
+                    ]
+                }
+            )
         return self.optimizers, [self.scheduler]
    
 
     def _clamp_inverse_problem_params(self):
         for v in self._params:
             self._params[v].data.clamp_(
-                    self.problem.unknown_parameter_domain.range_[v][0],
-                    self.problem.unknown_parameter_domain.range_[v][1])
+                self.problem.unknown_parameter_domain.range_[v][0],
+                self.problem.unknown_parameter_domain.range_[v][1],
+            )
 
     def _loss_data(self, input, output):
         return self.loss(self.forward(input), output)
@@ -209,9 +221,15 @@ 
    Source code for pina.solvers.pinn
         def _loss_phys(self, samples, equation):
         try:
             residual = equation.residual(samples, self.forward(samples))
-        except TypeError: # this occurs when the function has three inputs, i.e. inverse problem
-            residual = equation.residual(samples, self.forward(samples), self._params)
-        return self.loss(torch.zeros_like(residual, requires_grad=True), residual)
+        except (
+            TypeError
+        ):  # this occurs when the function has three inputs, i.e. inverse problem
+            residual = equation.residual(
+                samples, self.forward(samples), self._params
+            )
+        return self.loss(
+            torch.zeros_like(residual, requires_grad=True), residual
+        )
 
 
    [docs]    def training_step(self, batch, batch_idx):
         """
@@ -228,20 +246,25 @@ 
    Source code for pina.solvers.pinn
             dataloader = self.trainer.train_dataloader
         condition_losses = []
 
-        condition_idx = batch['condition']
+        condition_idx = batch["condition"]
 
-        for condition_id in range(condition_idx.min(), condition_idx.max()+1):
+        for condition_id in range(condition_idx.min(), condition_idx.max() + 1):
 
-            condition_name = dataloader.condition_names[condition_id]
+            if sys.version_info >= (3, 8):
+                condition_name = dataloader.condition_names[condition_id]
+            else:
+                condition_name = dataloader.loaders.condition_names[
+                    condition_id
+                ]
             condition = self.problem.conditions[condition_name]
-            pts = batch['pts']
+            pts = batch["pts"]
 
             if len(batch) == 2:
                 samples = pts[condition_idx == condition_id]
                 loss = self._loss_phys(samples, condition.equation)
             elif len(batch) == 3:
                 samples = pts[condition_idx == condition_id]
-                ground_truth = batch['output'][condition_idx == condition_id]
+                ground_truth = batch["output"][condition_idx == condition_id]
                 loss = self._loss_data(samples, ground_truth)
             else:
                 raise ValueError("Batch size not supported")
@@ -249,10 +272,16 @@ 
    Source code for pina.solvers.pinn
                 # TODO for users this us hard to remember when creating a new solver, to fix in a smarter way
             loss = loss.as_subclass(torch.Tensor)
 
-#            # add condition losses and accumulate logging for each epoch
+            #            # add condition losses and accumulate logging for each epoch
             condition_losses.append(loss * condition.data_weight)
-            self.log(condition_name + '_loss', float(loss),
-                     prog_bar=True, logger=True, on_epoch=True, on_step=False)
+            self.log(
+                condition_name + "_loss",
+                float(loss),
+                prog_bar=True,
+                logger=True,
+                on_epoch=True,
+                on_step=False,
+            )
 
         # clamp unknown parameters of the InverseProblem to their domain ranges (if needed)
         if isinstance(self.problem, InverseProblem):
@@ -261,8 +290,14 @@ 
    Source code for pina.solvers.pinn
             # TODO Fix the bug, tot_loss is a label tensor without labels
         # we need to pass it as a torch tensor to make everything work
         total_loss = sum(condition_losses)
-        self.log('mean_loss', float(total_loss / len(condition_losses)),
-                 prog_bar=True, logger=True, on_epoch=True, on_step=False)
+        self.log(
+            "mean_loss",
+            float(total_loss / len(condition_losses)),
+            prog_bar=True,
+            logger=True,
+            on_epoch=True,
+            on_step=False,
+        )
 
         return total_loss
    
 
@@ -295,8 +330,8 @@ 
    Source code for pina.solvers.pinn
       
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/solvers/solver.html b/_modules/pina/solvers/solver.html
index 3334419a..1dc7f4f2 100644
--- a/_modules/pina/solvers/solver.html
+++ b/_modules/pina/solvers/solver.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.solvers.solver — PINA 0.1 documentation
+  pina.solvers.solver — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -104,12 +106,14 @@ 
    Source code for pina.solvers.solver
         LightningModule methods.
     """
 
-    def __init__(self,
-                 models,
-                 problem,
-                 optimizers,
-                 optimizers_kwargs,
-                 extra_features=None):
+    def __init__(
+        self,
+        models,
+        problem,
+        optimizers,
+        optimizers_kwargs,
+        extra_features=None,
+    ):
         """
         :param models: A torch neural network model instance.
         :type models: torch.nn.Module
@@ -119,7 +123,7 @@ 
    Source code for pina.solvers.solver
                 use.
         :param list(dict) optimizer_kwargs: A list of optimizer constructor keyword args.
         :param list(torch.nn.Module) extra_features: The additional input
-            features to use as augmented input. If ``None`` no extra features 
+            features to use as augmented input. If ``None`` no extra features
             are passed. If it is a list of :class:`torch.nn.Module`, the extra feature
             list is passed to all models. If it is a list of extra features' lists,
             each single list of extra feature is passed to a model.
@@ -146,19 +150,23 @@ 
    Source code for pina.solvers.solver
     
         # check length consistency optimizers
         if len_model != len_optimizer:
-            raise ValueError('You must define one optimizer for each model.'
-                             f'Got {len_model} models, and {len_optimizer}'
-                             ' optimizers.')
+            raise ValueError(
+                "You must define one optimizer for each model."
+                f"Got {len_model} models, and {len_optimizer}"
+                " optimizers."
+            )
 
         # check length consistency optimizers kwargs
         if len_optimizer_kwargs != len_optimizer:
-            raise ValueError('You must define one dictionary of keyword'
-                             ' arguments for each optimizers.'
-                             f'Got {len_optimizer} optimizers, and'
-                             f' {len_optimizer_kwargs} dicitionaries')
+            raise ValueError(
+                "You must define one dictionary of keyword"
+                " arguments for each optimizers."
+                f"Got {len_optimizer} optimizers, and"
+                f" {len_optimizer_kwargs} dicitionaries"
+            )
 
         # extra features handling
-        if (extra_features is None) or (len(extra_features)==0):
+        if (extra_features is None) or (len(extra_features) == 0):
             extra_features = [None] * len_model
         else:
             # if we only have a list of extra features
@@ -167,24 +175,28 @@ 
    Source code for pina.solvers.solver
                 else:  # if we have a list of list extra features
                 if len(extra_features) != len_model:
                     raise ValueError(
-                        'You passed a list of extrafeatures list with len'
-                        f'different of models len. Expected {len_model} '
-                        f'got {len(extra_features)}. If you want to use '
-                        'the same list of extra features for all models, '
-                        'just pass a list of extrafeatures and not a list '
-                        'of list of extra features.')
+                        "You passed a list of extrafeatures list with len"
+                        f"different of models len. Expected {len_model} "
+                        f"got {len(extra_features)}. If you want to use "
+                        "the same list of extra features for all models, "
+                        "just pass a list of extrafeatures and not a list "
+                        "of list of extra features."
+                    )
 
         # assigning model and optimizers
         self._pina_models = []
         self._pina_optimizers = []
 
         for idx in range(len_model):
-            model_ = Network(model=models[idx],
-                             input_variables=problem.input_variables,
-                             output_variables=problem.output_variables,
-                             extra_features=extra_features[idx])
-            optim_ = optimizers[idx](model_.parameters(),
-                                     **optimizers_kwargs[idx])
+            model_ = Network(
+                model=models[idx],
+                input_variables=problem.input_variables,
+                output_variables=problem.output_variables,
+                extra_features=extra_features[idx],
+            )
+            optim_ = optimizers[idx](
+                model_.parameters(), **optimizers_kwargs[idx]
+            )
             self._pina_models.append(model_)
             self._pina_optimizers.append(optim_)
 
@@ -243,8 +255,8 @@ 
    Source code for pina.solvers.solver
       
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/solvers/supervised.html b/_modules/pina/solvers/supervised.html
index 5cc7761b..65c69ce1 100644
--- a/_modules/pina/solvers/supervised.html
+++ b/_modules/pina/solvers/supervised.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.solvers.supervised — PINA 0.1 documentation
+  pina.solvers.supervised — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -88,11 +90,16 @@
              
   
    Source code for pina.solvers.supervised
     """ Module for SupervisedSolver """
+
 import torch
+import sys
+
 try:
     from torch.optim.lr_scheduler import LRScheduler  # torch >= 2.0
 except ImportError:
-    from torch.optim.lr_scheduler import _LRScheduler as LRScheduler  # torch < 2.0
+    from torch.optim.lr_scheduler import (
+        _LRScheduler as LRScheduler,
+    )  # torch < 2.0
 
 from torch.optim.lr_scheduler import ConstantLR
 
@@ -106,7 +113,7 @@ 
    Source code for pina.solvers.supervised
     
    [docs]class SupervisedSolver(SolverInterface):
     """
     SupervisedSolver solver class. This class implements a SupervisedSolver,
-    using a user specified ``model`` to solve a specific ``problem``. 
+    using a user specified ``model`` to solve a specific ``problem``.
     """
 
     def __init__(
@@ -116,14 +123,11 @@ 
    Source code for pina.solvers.supervised
             extra_features=None,
         loss=torch.nn.MSELoss(),
         optimizer=torch.optim.Adam,
-        optimizer_kwargs={'lr': 0.001},
+        optimizer_kwargs={"lr": 0.001},
         scheduler=ConstantLR,
-        scheduler_kwargs={
-            "factor": 1,
-            "total_iters": 0
-        },
+        scheduler_kwargs={"factor": 1, "total_iters": 0},
     ):
-        '''
+        """
         :param AbstractProblem problem: The formualation of the problem.
         :param torch.nn.Module model: The neural network model to use.
         :param torch.nn.Module loss: The loss function used as minimizer,
@@ -137,12 +141,14 @@ 
    Source code for pina.solvers.supervised
             :param torch.optim.LRScheduler scheduler: Learning
             rate scheduler.
         :param dict scheduler_kwargs: LR scheduler constructor keyword args.
-        '''
-        super().__init__(models=[model],
-                         problem=problem,
-                         optimizers=[optimizer],
-                         optimizers_kwargs=[optimizer_kwargs],
-                         extra_features=extra_features)
+        """
+        super().__init__(
+            models=[model],
+            problem=problem,
+            optimizers=[optimizer],
+            optimizers_kwargs=[optimizer_kwargs],
+            extra_features=extra_features,
+        )
 
         # check consistency
         check_consistency(scheduler, LRScheduler, subclass=True)
@@ -157,7 +163,7 @@ 
    Source code for pina.solvers.supervised
     
    [docs]    def forward(self, x):
         """Forward pass implementation for the solver.
 
-        :param torch.Tensor x: Input tensor. 
+        :param torch.Tensor x: Input tensor.
         :return: Solver solution.
         :rtype: torch.Tensor
         """
@@ -183,29 +189,39 @@ 
    Source code for pina.solvers.supervised
             """
 
         dataloader = self.trainer.train_dataloader
-        condition_idx = batch['condition']
+        condition_idx = batch["condition"]
 
-        for condition_id in range(condition_idx.min(), condition_idx.max()+1):
+        for condition_id in range(condition_idx.min(), condition_idx.max() + 1):
 
-            condition_name = dataloader.condition_names[condition_id]
+            if sys.version_info >= (3, 8):
+                condition_name = dataloader.condition_names[condition_id]
+            else:
+                condition_name = dataloader.loaders.condition_names[
+                    condition_id
+                ]
             condition = self.problem.conditions[condition_name]
-            pts = batch['pts']
-            out = batch['output']
+            pts = batch["pts"]
+            out = batch["output"]
 
             if condition_name not in self.problem.conditions:
-                raise RuntimeError('Something wrong happened.')
+                raise RuntimeError("Something wrong happened.")
 
             # for data driven mode
-            if not hasattr(condition, 'output_points'):
-                raise NotImplementedError('Supervised solver works only in data-driven mode.')
-            
+            if not hasattr(condition, "output_points"):
+                raise NotImplementedError(
+                    "Supervised solver works only in data-driven mode."
+                )
+
             output_pts = out[condition_idx == condition_id]
             input_pts = pts[condition_idx == condition_id]
 
-            loss = self.loss(self.forward(input_pts), output_pts) * condition.data_weight
+            loss = (
+                self.loss(self.forward(input_pts), output_pts)
+                * condition.data_weight
+            )
             loss = loss.as_subclass(torch.Tensor)
 
-        self.log('mean_loss', float(loss), prog_bar=True, logger=True)
+        self.log("mean_loss", float(loss), prog_bar=True, logger=True)
         return loss
    
 
     @property
@@ -237,8 +253,8 @@ 
    Source code for pina.solvers.supervised
       
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_modules/pina/trainer.html b/_modules/pina/trainer.html
index 0bf3809b..08cda020 100644
--- a/_modules/pina/trainer.html
+++ b/_modules/pina/trainer.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  pina.trainer — PINA 0.1 documentation
+  pina.trainer — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -35,7 +37,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -94,6 +96,7 @@ 
    Source code for pina.trainer
     from .dataset import SamplePointDataset, SamplePointLoader, DataPointDataset
 from .solvers.solver import SolverInterface
 
+
 
    [docs]class Trainer(pytorch_lightning.Trainer):
 
     def __init__(self, solver, batch_size=None, **kwargs):
@@ -118,18 +121,20 @@ 
    Source code for pina.trainer
             check_consistency(solver, SolverInterface)
         if batch_size is not None:
             check_consistency(batch_size, int)
-        
+
         self._model = solver
         self.batch_size = batch_size
 
         # create dataloader
         if solver.problem.have_sampled_points is False:
-            raise RuntimeError(f'Input points in {solver.problem.not_sampled_points} '
-                               'training are None. Please '
-                               'sample points in your problem by calling '
-                               'discretise_domain function before train '
-                               'in the provided locations.')
-        
+            raise RuntimeError(
+                f"Input points in {solver.problem.not_sampled_points} "
+                "training are None. Please "
+                "sample points in your problem by calling "
+                "discretise_domain function before train "
+                "in the provided locations."
+            )
+
         self._create_or_update_loader()
 
     def _create_or_update_loader(self):
@@ -141,21 +146,23 @@ 
    Source code for pina.trainer
             devices = self._accelerator_connector._parallel_devices
 
         if len(devices) > 1:
-            raise RuntimeError('Parallel training is not supported yet.')
+            raise RuntimeError("Parallel training is not supported yet.")
 
         device = devices[0]
         dataset_phys = SamplePointDataset(self._model.problem, device)
         dataset_data = DataPointDataset(self._model.problem, device)
         self._loader = SamplePointLoader(
-            dataset_phys, dataset_data, batch_size=self.batch_size,
-            shuffle=True)
+            dataset_phys, dataset_data, batch_size=self.batch_size, shuffle=True
+        )
 
 
    [docs]    def train(self, **kwargs):
         """
         Train the solver method.
         """
-        return super().fit(self._model, train_dataloaders=self._loader, **kwargs)
    
-    
+        return super().fit(
+            self._model, train_dataloaders=self._loader, **kwargs
+        )
    
+
     @property
     def solver(self):
         """
@@ -171,8 +178,8 @@ 
    Source code for pina.trainer
       
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_rst/_code.html b/_rst/_code.html
index e7228b07..dc1cfd3f 100644
--- a/_rst/_code.html
+++ b/_rst/_code.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  Code Documentation — PINA 0.1 documentation
+  Code Documentation — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -37,7 +39,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
@@ -302,8 +308,8 @@ 
    Metrics and Losses
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_rst/_contributing.html b/_rst/_contributing.html
index 09d02162..683f2dbb 100644
--- a/_rst/_contributing.html
+++ b/_rst/_contributing.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  How to contribute — PINA 0.1 documentation
+  How to contribute — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -37,7 +39,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
 
diff --git a/_rst/_installation.html b/_rst/_installation.html
index ef1febc9..95560d8c 100644
--- a/_rst/_installation.html
+++ b/_rst/_installation.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  Installation — PINA 0.1 documentation
+  Installation — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -37,7 +39,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -131,8 +133,8 @@ 
    Installing from source
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_rst/_tutorial.html b/_rst/_tutorial.html
index dcc2b21f..53b57056 100644
--- a/_rst/_tutorial.html
+++ b/_rst/_tutorial.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  PINA Tutorials — PINA 0.1 documentation
+  PINA Tutorials — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -37,7 +39,7 @@
               
               
               
    
-                0.1
+                0.1.0.post2403
               
    
 
 
    
@@ -160,8 +164,8 @@ 
    Supervised Learning
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_rst/callbacks/adaptive_refinment_callbacks.html b/_rst/callbacks/adaptive_refinment_callbacks.html
index 35bc1ec6..3f869918 100644
--- a/_rst/callbacks/adaptive_refinment_callbacks.html
+++ b/_rst/callbacks/adaptive_refinment_callbacks.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  Adaptive Refinments callbacks — PINA 0.1 documentation
+  Adaptive Refinments callbacks — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -37,7 +39,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
 
diff --git a/_rst/callbacks/optimizer_callbacks.html b/_rst/callbacks/optimizer_callbacks.html
index 56a63b4c..830cd7a3 100644
--- a/_rst/callbacks/optimizer_callbacks.html
+++ b/_rst/callbacks/optimizer_callbacks.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  Optimizer callbacks — PINA 0.1 documentation
+  Optimizer callbacks — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -37,7 +39,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -119,7 +121,7 @@ 
    Optimizer callbacksParameters
 
    
 
diff --git a/_rst/callbacks/processing_callbacks.html b/_rst/callbacks/processing_callbacks.html
index 4001b87f..eb63c002 100644
--- a/_rst/callbacks/processing_callbacks.html
+++ b/_rst/callbacks/processing_callbacks.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  Processing callbacks — PINA 0.1 documentation
+  Processing callbacks — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -37,7 +39,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -183,8 +185,8 @@ 
    Processing callbacks
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_rst/condition.html b/_rst/condition.html
index 9a84bbbd..1b581546 100644
--- a/_rst/condition.html
+++ b/_rst/condition.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  Condition — PINA 0.1 documentation
+  Condition — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -37,7 +39,7 @@
               
               
               
    
-                0.1
+                0.1.0.post2403
               
    
 
 
diff --git a/_rst/equations.html b/_rst/equations.html
index da0dea94..4b3f2b93 100644
--- a/_rst/equations.html
+++ b/_rst/equations.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  Equations — PINA 0.1 documentation
+  Equations — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -37,7 +39,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
 
diff --git a/_rst/geometry/cartesian.html b/_rst/geometry/cartesian.html
index f4464f55..78973e36 100644
--- a/_rst/geometry/cartesian.html
+++ b/_rst/geometry/cartesian.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  CartesianDomain — PINA 0.1 documentation
+  CartesianDomain — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -37,7 +39,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -266,8 +268,8 @@
   
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_rst/geometry/difference_domain.html b/_rst/geometry/difference_domain.html
index 74db85dc..10dca0fa 100644
--- a/_rst/geometry/difference_domain.html
+++ b/_rst/geometry/difference_domain.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  Difference — PINA 0.1 documentation
+  Difference — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -37,7 +39,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -147,7 +149,7 @@
 
    
 
    Parameters
    
 
      
-
    • point (torch.Tensor) – Point to be checked.
      • 
+
    • point (torch.Tensor) – Point to be checked.
      • 
 
    • check_border (bool) – If True, the border is considered inside.
      • 
 
    
 
    
@@ -214,8 +216,8 @@
   
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_rst/geometry/ellipsoid.html b/_rst/geometry/ellipsoid.html
index 932d96a8..a4b3401d 100644
--- a/_rst/geometry/ellipsoid.html
+++ b/_rst/geometry/ellipsoid.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  EllipsoidDomain — PINA 0.1 documentation
+  EllipsoidDomain — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -37,7 +39,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -235,8 +237,8 @@
   
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_rst/geometry/exclusion_domain.html b/_rst/geometry/exclusion_domain.html
index 527bff9b..ca8352f8 100644
--- a/_rst/geometry/exclusion_domain.html
+++ b/_rst/geometry/exclusion_domain.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  Exclusion — PINA 0.1 documentation
+  Exclusion — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -37,7 +39,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -144,7 +146,7 @@
 
    
 
    Parameters
    
 
      
-
    • point (torch.Tensor) – Point to be checked.
      • 
+
    • point (torch.Tensor) – Point to be checked.
      • 
 
    • check_border (bool) – If True, the border is considered inside.
      • 
 
    
 
    
@@ -211,8 +213,8 @@
   
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_rst/geometry/intersection_domain.html b/_rst/geometry/intersection_domain.html
index 1cea05d3..67e30c05 100644
--- a/_rst/geometry/intersection_domain.html
+++ b/_rst/geometry/intersection_domain.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  Intersection — PINA 0.1 documentation
+  Intersection — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -37,7 +39,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -146,7 +148,7 @@
 
    
 
    Parameters
    
 
      
-
    • point (torch.Tensor) – Point to be checked.
      • 
+
    • point (torch.Tensor) – Point to be checked.
      • 
 
    • check_border (bool) – If True, the border is considered inside.
      • 
 
    
 
    
@@ -213,8 +215,8 @@
   
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_rst/geometry/location.html b/_rst/geometry/location.html
index 4aa3edd3..3df5a817 100644
--- a/_rst/geometry/location.html
+++ b/_rst/geometry/location.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  Location — PINA 0.1 documentation
+  Location — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -37,7 +39,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -131,7 +133,7 @@
 
    
 
    Parameters
    
 
    
@@ -238,7 +240,7 @@ 
    Continuous convolution\(N\) the number of points in the mesh, D the dimension
 of the problem.
    
-
  • X (torch.Tensor) – Input data. Expect tensor of shape
+
  • X (torch.Tensor) – Input data. Expect tensor of shape
 \([B, N_{in}, M,  D]\) where \(B\) is the batch_size,
 :math`N_{in}`is the number of input fields, \(M\) the number of points
 in the mesh, \(D\) the dimension of the problem.
    • 
@@ -251,7 +253,7 @@ 
    Continuous convolution\(D\) the dimension of the problem.
    
 
 
    Return type
    
-
    torch.Tensor
    
+
    torch.Tensor
    
 
    
 
    
 
    
@@ -273,7 +275,7 @@ 
    Continuous convolution\(N\) the number of points in the mesh, D the dimension
 of the problem.
    
-
  • X (torch.Tensor) – Input data. Expect tensor of shape
+
  • X (torch.Tensor) – Input data. Expect tensor of shape
 \([B, N_{in}, M,  D]\) where \(B\) is the batch_size,
 :math`N_{in}`is the number of input fields, \(M\) the number of points
 in the mesh, \(D\) the dimension of the problem.
    • 
@@ -286,7 +288,7 @@ 
    Continuous convolution\(D\) the dimension of the problem.
    
 
 
    Return type
    
-
    torch.Tensor
    
+
    torch.Tensor
    
 
    
 
    
 
    
@@ -311,8 +313,8 @@ 
    Continuous convolution
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_rst/layers/enhanced_linear.html b/_rst/layers/enhanced_linear.html
index 9ec4b1b1..1ec3964b 100644
--- a/_rst/layers/enhanced_linear.html
+++ b/_rst/layers/enhanced_linear.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  EnhancedLinear — PINA 0.1 documentation
+  EnhancedLinear — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -37,7 +39,7 @@
               
               
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -113,13 +115,13 @@ 
    EnhancedLinear
 
    
 class EnhancedLinear(layer, activation=None, dropout=None)[source]
    
-
    Bases: torch.nn.modules.module.Module
    
+
    Bases: torch.nn.modules.module.Module
    
 
    A wrapper class for enhancing a linear layer with activation and/or dropout.
    
 
    
 
    Parameters
    
 
      
-
    • layer (torch.nn.Module) – The linear layer to be enhanced.
      • 
-
    • activation (torch.nn.Module) – The activation function to be applied after the linear layer.
      • 
+
    • layer (torch.nn.Module) – The linear layer to be enhanced.
      • 
+
    • activation (torch.nn.Module) – The activation function to be applied after the linear layer.
      • 
 
    • dropout (float) – The dropout probability to be applied after the activation (if provided).
      • 
 
    
 
    
@@ -136,8 +138,8 @@ 
    EnhancedLinear
 
    Parameters
    
 
      
-
    • layer (torch.nn.Module) – The linear layer to be enhanced.
      • 
-
    • activation (torch.nn.Module) – The activation function to be applied after the linear layer.
      • 
+
    • layer (torch.nn.Module) – The linear layer to be enhanced.
      • 
+
    • activation (torch.nn.Module) – The activation function to be applied after the linear layer.
      • 
 
    • dropout (float) – The dropout probability to be applied after the activation (if provided).
      • 
 
    
 
    
@@ -148,13 +150,13 @@ 
    EnhancedLinear
 
    Parameters
    
-
    x (torch.Tensor) – Input tensor.
    
+
    x (torch.Tensor) – Input tensor.
    
 
    
 
    Returns
    
 
    Output tensor after passing through the enhanced linear module.
    
 
    
 
    Return type
    
-
    torch.Tensor
    
+
    torch.Tensor
    
 
    
 
    
 
    
@@ -174,8 +176,8 @@ 
    EnhancedLinear
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_rst/layers/fourier.html b/_rst/layers/fourier.html
index 31b0bb0e..165da7a0 100644
--- a/_rst/layers/fourier.html
+++ b/_rst/layers/fourier.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  Fourier Layers — PINA 0.1 documentation
+  Fourier Layers — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -37,7 +39,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -113,7 +115,7 @@ 
    Fourier Layers
 
    
 class FourierBlock1D(input_numb_fields, output_numb_fields, n_modes, activation=<class 'torch.nn.modules.activation.Tanh'>)[source]
    
-
    Bases: torch.nn.modules.module.Module
    
+
    Bases: torch.nn.modules.module.Module
    
 
    Fourier block implementation for three dimensional
 input tensor. The combination of Fourier blocks
 make up the Fourier Neural Operator
    
@@ -124,7 +126,7 @@ 
    Fourier LayersarXiv preprint arXiv:2010.08895.
    
 
    
-
    Initializes internal Module state, shared by both nn.Module and ScriptModule.
    
+
    Initialize internal Module state, shared by both nn.Module and ScriptModule.
    
 
    
 
    
 forward(x)[source]
    
@@ -133,7 +135,7 @@ 
    Fourier Layers
 
    Parameters
    
-
    x (torch.Tensor) – The input tensor for fourier block, expect of size
+
    x (torch.Tensor) – The input tensor for fourier block, expect of size
 [batch, input_numb_fields, x].
    
 
    
 
    Returns
    
@@ -141,7 +143,7 @@ 
    Fourier Layers[batch, output_numb_fields, x].
    
 
 
    Return type
    
-
    torch.Tensor
    
+
    torch.Tensor
    
 
    
 
    
 
@@ -151,7 +153,7 @@ 
    Fourier Layers
 
    
 class FourierBlock2D(input_numb_fields, output_numb_fields, n_modes, activation=<class 'torch.nn.modules.activation.Tanh'>)[source]
    
-
    Bases: torch.nn.modules.module.Module
    
+
    Bases: torch.nn.modules.module.Module
    
 
    Fourier block implementation for two dimensional
 input tensor. The combination of Fourier blocks
 make up the Fourier Neural Operator
    
@@ -178,7 +180,7 @@ 
    Fourier Layersint) – The number of channels for the output.
    
 
  • | tuple n_modes (list) – Number of modes to select for each dimension.
 It must be at most equal to the floor(Nx/2)+1 and floor(Ny/2)+1.
    • 
-
  • activation (torch.nn.Module) – The activation function.
    • 
+
  • activation (torch.nn.Module) – The activation function.
    • 
 
 
    
 
@@ -190,7 +192,7 @@ 
    Fourier Layers
 
    Parameters
    
-
    x (torch.Tensor) – The input tensor for fourier block, expect of size
+
    x (torch.Tensor) – The input tensor for fourier block, expect of size
 [batch, input_numb_fields, x, y].
    
 
    
 
    Returns
    
@@ -198,7 +200,7 @@ 
    Fourier Layers[batch, output_numb_fields, x, y, z].
    
 
 
    Return type
    
-
    torch.Tensor
    
+
    torch.Tensor
    
 
    
 
 
@@ -208,7 +210,7 @@ 
    Fourier Layers
 
    
 class FourierBlock3D(input_numb_fields, output_numb_fields, n_modes, activation=<class 'torch.nn.modules.activation.Tanh'>)[source]
    
-
    Bases: torch.nn.modules.module.Module
    
+
    Bases: torch.nn.modules.module.Module
    
 
    Fourier block implementation for three dimensional
 input tensor. The combination of Fourier blocks
 make up the Fourier Neural Operator
    
@@ -236,7 +238,7 @@ 
    Fourier Layerslist) – Number of modes to select for each dimension.
 It must be at most equal to the floor(Nx/2)+1, floor(Ny/2)+1
 and floor(Nz/2)+1.
    
-
  • activation (torch.nn.Module) – The activation function.
    • 
+
  • activation (torch.nn.Module) – The activation function.
    • 
 
 
    
 
@@ -248,7 +250,7 @@ 
    Fourier Layers
 
    Parameters
    
-
    x (torch.Tensor) – The input tensor for fourier block, expect of size
+
    x (torch.Tensor) – The input tensor for fourier block, expect of size
 [batch, input_numb_fields, x, y, z].
    
 
    
 
    Returns
    
@@ -256,7 +258,7 @@ 
    Fourier Layers[batch, output_numb_fields, x, y, z].
    
 
 
    Return type
    
-
    torch.Tensor
    
+
    torch.Tensor
    
 
    
 
 
@@ -276,8 +278,8 @@ 
    Fourier Layers
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_rst/layers/residual.html b/_rst/layers/residual.html
index a26c0fc1..43e74711 100644
--- a/_rst/layers/residual.html
+++ b/_rst/layers/residual.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  Residual layer — PINA 0.1 documentation
+  Residual layer — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -37,7 +39,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -113,7 +115,7 @@ 
    Residual layer
 
    
 class ResidualBlock(input_dim, output_dim, hidden_dim, spectral_norm=False, activation=ReLU())[source]
    
-
    Bases: torch.nn.modules.module.Module
    
+
    Bases: torch.nn.modules.module.Module
    
 
    Residual block base class. Implementation of a residual block.
    
 
    
 
    See also
    
@@ -135,7 +137,7 @@ 
    Residual layerbool) – Apply spectral normalization to feedforward
 layers, defaults to False.
    
-
  • activation (torch.nn.Module) – Cctivation function after first block.
    • 
+
  • activation (torch.nn.Module) – Cctivation function after first block.
    • 
 
 
    
 
@@ -145,13 +147,13 @@ 
    Residual layer
 
    Parameters
    
-
    x (torch.Tensor) – Input tensor for the residual layer.
    
+
    x (torch.Tensor) – Input tensor for the residual layer.
    
 
    
 
    Returns
    
 
    Output tensor for the residual layer.
    
 
    
 
    Return type
    
-
    torch.Tensor
    
+
    torch.Tensor
    
 
    
 
 
@@ -171,8 +173,8 @@ 
    Residual layer
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_rst/layers/spectral.html b/_rst/layers/spectral.html
index 948b4da0..bd5c2310 100644
--- a/_rst/layers/spectral.html
+++ b/_rst/layers/spectral.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  Spectral Convolution — PINA 0.1 documentation
+  Spectral Convolution — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -37,7 +39,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -113,7 +115,7 @@ 
    Spectral Convolution
 
    
 class SpectralConvBlock1D(input_numb_fields, output_numb_fields, n_modes)[source]
    
-
    Bases: torch.nn.modules.module.Module
    
+
    Bases: torch.nn.modules.module.Module
    
 
    PINA implementation of Spectral Convolution Block for one
 dimensional tensors.
    
 
    The module computes the spectral convolution of the input with a linear kernel in the
@@ -137,7 +139,7 @@ 
    Spectral Convolution
    Forward computation for Spectral Convolution.
    
 
    
 
    Parameters
    
-
    x (torch.Tensor) – The input tensor, expect of size
+
    x (torch.Tensor) – The input tensor, expect of size
 [batch, input_numb_fields, x].
    
 
    
 
    Returns
    
@@ -145,7 +147,7 @@ 
    Spectral Convolution[batch, output_numb_fields, x].
    
 
    
 
    Return type
    
-
    torch.Tensor
    
+
    torch.Tensor
    
 
    
 
 
@@ -155,7 +157,7 @@ 
    Spectral Convolution
 
    
 class SpectralConvBlock2D(input_numb_fields, output_numb_fields, n_modes)[source]
    
-
    Bases: torch.nn.modules.module.Module
    
+
    Bases: torch.nn.modules.module.Module
    
 
    PINA implementation of spectral convolution block for two
 dimensional tensors.
    
 
    The module computes the spectral convolution of the input with a linear kernel in the
@@ -179,7 +181,7 @@ 
    Spectral Convolution
    Forward computation for Spectral Convolution.
    
 
    
 
    Parameters
    
-
    x (torch.Tensor) – The input tensor, expect of size
+
    x (torch.Tensor) – The input tensor, expect of size
 [batch, input_numb_fields, x, y].
    
 
    
 
    Returns
    
@@ -187,7 +189,7 @@ 
    Spectral Convolution[batch, output_numb_fields, x, y].
    
 
    
 
    Return type
    
-
    torch.Tensor
    
+
    torch.Tensor
    
 
    
 
 
@@ -197,7 +199,7 @@ 
    Spectral Convolution
 
    
 class SpectralConvBlock3D(input_numb_fields, output_numb_fields, n_modes)[source]
    
-
    Bases: torch.nn.modules.module.Module
    
+
    Bases: torch.nn.modules.module.Module
    
 
    PINA implementation of spectral convolution block for three
 dimensional tensors.
    
 
    The module computes the spectral convolution of the input with a linear kernel in the
@@ -222,7 +224,7 @@ 
    Spectral Convolution
    Forward computation for Spectral Convolution.
    
 
    
 
    Parameters
    
-
    x (torch.Tensor) – The input tensor, expect of size
+
    x (torch.Tensor) – The input tensor, expect of size
 [batch, input_numb_fields, x, y, z].
    
 
    
 
    Returns
    
@@ -230,7 +232,7 @@ 
    Spectral Convolution[batch, output_numb_fields, x, y, z].
    
 
    
 
    Return type
    
-
    torch.Tensor
    
+
    torch.Tensor
    
 
    
 
 
@@ -250,8 +252,8 @@ 
    Spectral Convolution
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_rst/loss/loss_interface.html b/_rst/loss/loss_interface.html
index 737c8dfd..404f387e 100644
--- a/_rst/loss/loss_interface.html
+++ b/_rst/loss/loss_interface.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  LpLoss — PINA 0.1 documentation
+  LpLoss — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -37,7 +39,7 @@
               
               
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -133,15 +135,15 @@
 
    
 
    Parameters
    
 
    
 
    
 
    Returns
    
 
    Loss evaluation.
    
 
    
 
    Return type
    
-
    torch.Tensor
    
+
    torch.Tensor
    
 
    
 
    
 
@@ -161,8 +163,8 @@
   
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_rst/loss/lploss.html b/_rst/loss/lploss.html
index 18018fb2..e9847277 100644
--- a/_rst/loss/lploss.html
+++ b/_rst/loss/lploss.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  LpLoss — PINA 0.1 documentation
+  LpLoss — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -37,7 +39,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -158,15 +160,15 @@ 
    LpLoss
 
    Parameters
    
 
    
 
    
 
    Returns
    
 
    Loss evaluation.
    
 
    
 
    Return type
    
-
    torch.Tensor
    
+
    torch.Tensor
    
 
    
 
 
@@ -186,8 +188,8 @@ 
    LpLoss
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_rst/loss/powerloss.html b/_rst/loss/powerloss.html
index 1e719071..e98c6474 100644
--- a/_rst/loss/powerloss.html
+++ b/_rst/loss/powerloss.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  PowerLoss — PINA 0.1 documentation
+  PowerLoss — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -37,7 +39,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -158,15 +160,15 @@ 
    PowerLoss
 
    Parameters
    
 
    
 
    
 
    Returns
    
 
    Loss evaluation.
    
 
    
 
    Return type
    
-
    torch.Tensor
    
+
    torch.Tensor
    
 
    
 
 
@@ -186,8 +188,8 @@ 
    PowerLoss
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_rst/models/base_no.html b/_rst/models/base_no.html
new file mode 100644
index 00000000..2b97e451
--- /dev/null
+++ b/_rst/models/base_no.html
@@ -0,0 +1,250 @@
+
+
+
+  
+  
+  KernelNeuralOperator — PINA 0.1.0.post2403 documentation
+    
+      
+
+  
+  
+  
+        
+        
+        
+        
+        
+        
+        
+    
+    
+    
+    
+     
+
+
+ 
+  
    
+    
+
+    
    
+
+      
    
+        
    
+          
    
+  
+  
    
+
    
+          
    
+           
    
+             
+  
    
+
    KernelNeuralOperator
    
+
    
+
    
+class KernelNeuralOperator(lifting_operator, integral_kernels, projection_operator)[source]
    
+
    Bases: torch.nn.modules.module.Module
    
+
    Base class for composing Neural Operators with integral kernels.
    
+
    This is a base class for composing neural operators with multiple
+integral kernels. All neural operator models defined in PINA inherit
+from this class. The structure is inspired by the work of Kovachki, N.
+et al. see Figure 2 of the reference for extra details. The Neural
+Operators inheriting from this class can be written as:
    
+
    
+\[G_\theta  := P \circ K_m \circ \cdot \circ K_1 \circ L\]
    
+
    where:
    
+
      
+
    • \(G_\theta: \mathcal{A}\subset \mathbb{R}^{\rm{in}} \rightarrow
+\mathcal{D}\subset \mathbb{R}^{\rm{out}}\) is the neural operator
+approximation of the unknown real operator \(G\), that is
+\(G \approx G_\theta\)
      • 
+
    • \(L: \mathcal{A}\subset \mathbb{R}^{\rm{in}} \rightarrow
+\mathbb{R}^{\rm{emb}}\) is a lifting operator mapping the input
+from its domain \(\mathcal{A}\subset \mathbb{R}^{\rm{in}}\)
+to its embedding dimension \(\mathbb{R}^{\rm{emb}}\)
      • 
+
    • \(\{K_i : \mathbb{R}^{\rm{emb}} \rightarrow
+\mathbb{R}^{\rm{emb}} \}_{i=1}^m\) are \(m\) integral kernels
+mapping each hidden representation to the next one.
      • 
+
    • \(P : \mathbb{R}^{\rm{emb}} \rightarrow  \mathcal{D}\subset
+\mathbb{R}^{\rm{out}}\) is a projection operator mapping the hidden
+representation to the output function.
      • 
+
    
+
    
+
    See also
    
+
    Original reference: Kovachki, N., Li, Z., Liu, B.,
+Azizzadenesheli, K., Bhattacharya, K., Stuart, A., & Anandkumar, A.
+(2023). Neural operator: Learning maps between function
+spaces with applications to PDEs. Journal of Machine Learning
+Research, 24(89), 1-97.
    
+
    
+
    
+
    Parameters
    
+
      
+
    • lifting_operator (torch.nn.Module) – The lifting operator
+mapping the input to its hidden dimension.
      • 
+
    • integral_kernels (torch.nn.Module) – List of integral kernels
+mapping each hidden representation to the next one.
      • 
+
    • projection_operator (torch.nn.Module) – The projection operator
+mapping the hidden representation to the output function.
      • 
+
    
+
    
+
    
+
    
+
    
+property lifting_operator
    
+
    The lifting operator property.
    
+
    
+
+
    
+
    
+property projection_operator
    
+
    The projection operator property.
    
+
    
+
+
    
+
    
+property integral_kernels
    
+
    The integral kernels operator property.
    
+
    
+
+
    
+
    
+forward(x)[source]
    
+
    Forward computation for Base Neural Operator. It performs a
+lifting of the input by the lifting_operator.
+Then different layers integral kernels are applied using
+integral_kernels. Finally the output is projected
+to the final dimensionality by the projection_operator.
    
+
    
+
    Parameters
    
+
    x (torch.Tensor) – The input tensor for performing the
+computation. It expects a tensor \(B \times N \times D\),
+where \(B\) is the batch_size, \(N\) the number of points
+in the mesh, \(D\) the dimension of the problem. In particular
+\(D\) is the number of spatial/paramtric/temporal variables
+plus the field variables. For example for 2D problems with 2
+outputvariables \(D=4\).
    
+
    
+
    Returns
    
+
    The output tensor obtained from the NO.
    
+
    
+
    Return type
    
+
    torch.Tensor
    
+
    
+
    
+
    
+
+
    
+
+
    
+
+
+           
    
+          
    
+          
    
+
+  
    
+
+  
    
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
+      
    
+  
    
+
+  Built with Sphinx using a
+    theme
+    provided by Read the Docs.
+   
+
+
    
+        
    
+      
    
+    
    
+  
    
+   
+
+
+
\ No newline at end of file
diff --git a/_rst/models/deeponet.html b/_rst/models/deeponet.html
index 937cebb4..9aa7b220 100644
--- a/_rst/models/deeponet.html
+++ b/_rst/models/deeponet.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  DeepONet — PINA 0.1 documentation
+  DeepONet — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -37,7 +39,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
    
@@ -54,11 +56,13 @@
 
  • Solvers
    • 
 
  • Models
 
    • 
@@ -131,13 +135,13 @@ 
    DeepONet
 
    Parameters
    
 
    
@@ -221,7 +225,7 @@ 
    DeepONet
    The output computed by the DeepONet model.
    
 
 
    Return type
    
-
    LabelTensor or torch.Tensor
    
+
    LabelTensor or torch.Tensor
    
 
    
 
 
@@ -253,8 +257,8 @@ 
    DeepONet
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_rst/models/fnn.html b/_rst/models/fnn.html
index b8c6f8cd..f5facb27 100644
--- a/_rst/models/fnn.html
+++ b/_rst/models/fnn.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  FeedForward — PINA 0.1 documentation
+  FeedForward — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -21,7 +23,7 @@
     
     
     
-     
+     
 
 
  
@@ -37,7 +39,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -54,11 +56,13 @@
 
  • Solvers
    • 
 
  • Models
 
    • 
@@ -115,7 +119,7 @@ 
    FeedForward
 
    
 class FeedForward(input_dimensions, output_dimensions, inner_size=20, n_layers=2, func=<class 'torch.nn.modules.activation.Tanh'>, layers=None, bias=True)[source]
    
-
    Bases: torch.nn.modules.module.Module
    
+
    Bases: torch.nn.modules.module.Module
    
 
    The PINA implementation of feedforward network, also refered as multilayer
 perceptron.
    
 
    
@@ -131,7 +135,7 @@ 
    FeedForwardint) – number of hidden layers. Default is 2.
    
 
  • func – the activation function to use. If a single
-torch.nn.Module is passed, this is used as activation function
+torch.nn.Module is passed, this is used as activation function
 after any layers, except the last one. If a list of Modules is passed,
 they are used as activation functions at any layers, in order.
    • 
 
  • | tuple(int) layers (list(int)) – a list containing the number of neurons for
@@ -147,13 +151,13 @@ 
    FeedForward
 
    Parameters
    
-
    x (torch.Tensor) – The tensor to apply the forward pass.
    
+
    x (torch.Tensor) – The tensor to apply the forward pass.
    
 
    
 
    Returns
    
 
    the output computed by the model.
    
 
    
 
    Return type
    
-
    torch.Tensor
    
+
    torch.Tensor
    
 
    
 
    • 
 
    
@@ -166,15 +170,15 @@ 
    FeedForward
-        
+        
         
     
    
 
   
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_rst/models/fnn_residual.html b/_rst/models/fnn_residual.html
index 1d01a726..3f7ae464 100644
--- a/_rst/models/fnn_residual.html
+++ b/_rst/models/fnn_residual.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  ResidualFeedForward — PINA 0.1 documentation
+  ResidualFeedForward — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -37,7 +39,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -54,11 +56,13 @@
 
  • Solvers
    • 
 
  • Models
 
    • 
@@ -115,7 +119,7 @@ 
    ResidualFeedForward
 
    
 class ResidualFeedForward(input_dimensions, output_dimensions, inner_size=20, n_layers=2, func=<class 'torch.nn.modules.activation.Tanh'>, bias=True, transformer_nets=None)[source]
    
-
    Bases: torch.nn.modules.module.Module
    
+
    Bases: torch.nn.modules.module.Module
    
 
    The PINA implementation of feedforward network, also with skipped connection
 and transformer network, as presented in Understanding and mitigating gradient
 pathologies in physics-informed neural networks
    
@@ -139,7 +143,7 @@ 
    ResidualFeedForwardint) – number of hidden layers. Default is 2.
    
 
  • func – the activation function to use. If a single
-torch.nn.Module is passed, this is used as activation function
+torch.nn.Module is passed, this is used as activation function
 after any layers, except the last one. If a list of Modules is passed,
 they are used as activation functions at any layers, in order.
    • 
 
  • bias (bool) – If True the MLP will consider some bias.
    • 
@@ -156,13 +160,13 @@ 
    ResidualFeedForward
 
    Parameters
    
-
    x (torch.Tensor) – The tensor to apply the forward pass.
    
+
    x (torch.Tensor) – The tensor to apply the forward pass.
    
 
    
 
    Returns
    
 
    the output computed by the model.
    
 
    
 
    Return type
    
-
    torch.Tensor
    
+
    torch.Tensor
    
 
    
 
 
    
@@ -182,8 +186,8 @@ 
    ResidualFeedForward
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_rst/models/fno.html b/_rst/models/fno.html
index 2ec15fb2..bf01dc94 100644
--- a/_rst/models/fno.html
+++ b/_rst/models/fno.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  FNO — PINA 0.1 documentation
+  FNO — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -21,7 +23,7 @@
     
     
     
-     
+     
 
 
  
@@ -37,7 +39,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -54,11 +56,13 @@
 
  • Solvers
    • 
 
  • Models
 
    • 
@@ -115,21 +119,39 @@ 
    FNO
 
    
 class FNO(lifting_net, projecting_net, n_modes, dimensions=3, padding=8, padding_type='constant', inner_size=20, n_layers=2, func=<class 'torch.nn.modules.activation.Tanh'>, layers=None)[source]
    
-
    Bases: torch.nn.modules.module.Module
    
+
    Bases: pina.model.base_no.KernelNeuralOperator
    
 
    The PINA implementation of Fourier Neural Operator network.
    
-
    Fourier Neural Operator (FNO) is a general architecture for learning Operators.
-Unlike traditional machine learning methods FNO is designed to map
-entire functions to other functions. It can be trained both with
-Supervised learning strategies. FNO does global convolution by performing the
-operation on the Fourier space.
    
+
    Fourier Neural Operator (FNO) is a general architecture for
+learning Operators. Unlike traditional machine learning methods
+FNO is designed to map entire functions to other functions. It
+can be trained with Supervised learning strategies. FNO does global
+convolution by performing the operation on the Fourier space.
    
 
    
 
    See also
    
-
    Original reference: Li, Z., Kovachki, N., Azizzadenesheli, K., Liu, B.,
-Bhattacharya, K., Stuart, A., & Anandkumar, A. (2020). Fourier neural operator for
-parametric partial differential equations.
+
    Original reference: Li, Z., Kovachki, N., Azizzadenesheli,
+K., Liu, B., Bhattacharya, K., Stuart, A., & Anandkumar, A.
+(2020). Fourier neural operator for parametric partial
+differential equations.
 DOI: arXiv preprint arXiv:2010.08895.
    
 
    
-
    Initializes internal Module state, shared by both nn.Module and ScriptModule.
    
+
    
+
    Parameters
    
+
      
+
    • lifting_net (torch.nn.Module) – The neural network for lifting
+the input.
      • 
+
    • projecting_net (torch.nn.Module) – The neural network for
+projecting the output.
      • 
+
    • | list[int] n_modes (int) – Number of modes.
      • 
+
    • dimensions (int) – Number of dimensions (1, 2, or 3).
      • 
+
    • padding (int) – Padding size, defaults to 8.
      • 
+
    • padding_type (str) – Type of padding, defaults to constant.
      • 
+
    • inner_size (int) – Inner size, defaults to 20.
      • 
+
    • n_layers (int) – Number of layers, defaults to 2.
      • 
+
    • func (torch.nn.Module) – Activation function, defaults to nn.Tanh.
      • 
+
    • layers (list[int]) – List of layer sizes, defaults to None.
      • 
+
    
+
    
+
    
 
    
 
    
 forward(x)[source]
    
@@ -139,17 +161,21 @@ 
    FNOprojecting_net.
    
 
    
 
    Parameters
    
-
    x (torch.Tensor) – The input tensor for fourier block, depending on
-dimension in the initialization. In particular it is expected
-* 1D tensors: [batch, X, channels]
-* 2D tensors: [batch, X, Y, channels]
-* 3D tensors: [batch, X, Y, Z, channels]
    
+
    x (torch.Tensor) – 
    The input tensor for fourier block,
+depending on dimension in the initialization. In
+particular it is expected:
    
+
      
+
    • 1D tensors: [batch, X, channels]
      • 
+
    • 2D tensors: [batch, X, Y, channels]
      • 
+
    • 3D tensors: [batch, X, Y, Z, channels]
      • 
+
    
+
    
 
    
 
    Returns
    
-
    The output tensor obtained from the FNO.
    
+
    The output tensor obtained from FNO.
    
 
    
 
    Return type
    
-
    torch.Tensor
    
+
    torch.Tensor
    
 
    
 
    
 
    
@@ -162,15 +188,15 @@ 
    FNO
           
    
           
    
 
   
    
 
   
    
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_rst/models/multifeedforward.html b/_rst/models/multifeedforward.html
index 26d5f6db..7cd96d17 100644
--- a/_rst/models/multifeedforward.html
+++ b/_rst/models/multifeedforward.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  MultiFeedForward — PINA 0.1 documentation
+  MultiFeedForward — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -37,7 +39,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -54,11 +56,13 @@
 
  • Solvers
    • 
 
  • Models
 
    • 
@@ -115,7 +119,7 @@ 
    MultiFeedForward
 
    
 class MultiFeedForward(ffn_dict)[source]
    
-
    Bases: torch.nn.modules.module.Module
    
+
    Bases: torch.nn.modules.module.Module
    
 
    The PINA implementation of MultiFeedForward network.
    
 
    This model allows to create a network with multiple FeedForward combined
 together. The user has to define the forward method choosing how to
@@ -125,7 +129,7 @@ 
    MultiFeedForward
    ffn_dict (dict) – dictionary of FeedForward networks.
    
 
    
 
-
    Initializes internal Module state, shared by both nn.Module and ScriptModule.
    
+
    Initialize internal Module state, shared by both nn.Module and ScriptModule.
    
 
 
 
    
@@ -141,8 +145,8 @@ 
    MultiFeedForward
-    
    © Copyright Copyright 2021-2023, PINA Contributors.
-      Last updated on Nov 17, 2023.
+    
    © Copyright Copyright 2021-2024, PINA Contributors.
+      Last updated on Mar 01, 2024.
       
    
   
    
 
diff --git a/_rst/models/network.html b/_rst/models/network.html
index 9cff1bfa..33df3751 100644
--- a/_rst/models/network.html
+++ b/_rst/models/network.html
@@ -1,11 +1,13 @@
 
-
+
 
   
   
-  Network — PINA 0.1 documentation
+  Network — PINA 0.1.0.post2403 documentation
     
-      
+      
+
+  
   
@@ -20,7 +22,7 @@
     
     
     
-    
+    
      
 
 
@@ -37,7 +39,7 @@
               
           
               
    
-                0.1
+                0.1.0.post2403
               
    
 
    
   
@@ -54,11 +56,13 @@
 
  • Solvers
    • 
 
  • Models
 
    • 
@@ -115,20 +119,20 @@
 
    
 
    
 class Network(model, input_variables, output_variables, extra_features=None)[source]
    
-
    Bases: torch.nn.modules.module.Module
    
+
    Bases: torch.nn.modules.module.Module
    
 
    Network class with standard forward method
 and possibility to pass extra features. This
 class is used internally in PINA to convert
-any torch.nn.Module s in a PINA module.
    
+any torch.nn.Module s in a PINA module.
    
 
    
 
    Parameters
    
 
      
-
    • model (torch.nn.Module) – The torch model to convert in a PINA model.
      • 
+
    • model (torch.nn.Module) – The torch model to convert in a PINA model.
      • 
 
    • input_variables (list(str)) – The input variables of the AbstractProblem, whose type depends on the
 type of domain (spatial, temporal, and parameter).
      • 
 
    • output_variables (list(str)) – The output variables of the AbstractProblem, whose type depends on the
 problem setting.
      • 
-
    • extra_features (list(torch.nn.Module)) – List of torch models to augment the input, defaults to None.
      • 
+
    • extra_features (list(torch.nn.Module)) – List of torch models to augment the input, defaults to None.
      • 
 
    
 
    
 
    
@@ -143,7 +147,7 @@
 extraction.
    
 
    
 
    Parameters
    
-
    x (torch.Tensor) – Input of the network.
    
+
    x (torch.Tensor) – Input of the network.
    
 
    
 
    Return torch.Tensor
    
 
    Output of the network.
    
@@ -184,14 +188,14 @@

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