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Force constants calculation using pypolymlp (machine learning potential)

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Force constants calculation using pypolymlp (machine learning potential)#

+

This is an experimental feature.

+

With the --pypolymlp option, phono3py can interface with the polynomial +machine learning potential (MLP) code, +pypolymlp, to perform training and +evaluation tasks of MLPs. This feature aims to reduce the computational cost of +anharmonic force constant calculations by using MLPs as an intermediary layer, +efficiently representing atomic interactions.

+

The training process involves using a dataset consisting of supercell +displacements, forces, and energies. The trained MLPs are then employed to +compute forces for supercells with specific displacements.

+

For more details on the methodology, refer to A. Togo and A. Seko, J. Chem. Phys. +160, 211001 (2024) [doi].

+

An example of its usage can be found in the example/NaCl-pypolymlp directory +in the distribution from GitHub or PyPI.

+
+

Requirement#

+ +
+
+

Workflow#

+
    +

  1. Generate random displacements in supercells. Use –rd option.

    2. +

  2. Calculate corresponding forces and energies in supercells. Use of VASP +interface is recommended for –sp option is supported.

    3. +

  3. Prepare dataset composed of displacements, forces, and energies in +supercells. The dataset must be stored in a phono3py-yaml-like file, e.g., +phono3py_params.yaml. Use –cf3 and –sp option simultaneously.

    4. +

  4. Develop MLPs. At this step phono3py.pmlp is saved.

    5. +

  5. Generate displacements in supercells either systematic or random displacements.

    6. +

  6. Evaluate MLPs for forces of the supercells generated in step 5.

    7. +

  7. Calculate force constants from displacement-force dataset from steps 5 and 6.

    8. +
+

The steps 4-7 are executed in running phono3py with --pypolymlp +option.

+
+

Steps 1-3: Dataset preparation#

+

For the training, the following supercell data are required in the phono3py +setting to use pypolymlp:

+
    +

  • Displacements

    • +

  • Forces

    • +

  • Total energies

    • +
+

These data must be stored in phono3py.yaml-like file.

+

The supercells with displacements are generated by

+
% phono3py --pa auto --rd 100 -c POSCAR-unitcell --dim 2 2 2
+        _                      _____
+  _ __ | |__   ___  _ __   ___|___ / _ __  _   _
+ | '_ \| '_ \ / _ \| '_ \ / _ \ |_ \| '_ \| | | |
+ | |_) | | | | (_) | | | | (_) |__) | |_) | |_| |
+ | .__/|_| |_|\___/|_| |_|\___/____/| .__/ \__, |
+ |_|                                |_|    |___/
+                                           3.5.0
+
+-------------------------[time 2024-09-19 14:40:00]-------------------------
+Compiled with OpenMP support (max 10 threads).
+Python version 3.12.4
+Spglib version 2.5.0
+
+Unit cell was read from "POSCAR-unitcell".
+-------------------------------- unit cell ---------------------------------
+Lattice vectors:
+  a    5.603287477054753    0.000000000000000    0.000000000000000
+  b    0.000000000000000    5.603287477054753    0.000000000000000
+  c    0.000000000000000    0.000000000000000    5.603287477054753
+Atomic positions (fractional):
+    1 Na  0.00000000000000  0.00000000000000  0.00000000000000  22.990
+    2 Na  0.00000000000000  0.50000000000000  0.50000000000000  22.990
+    3 Na  0.50000000000000  0.00000000000000  0.50000000000000  22.990
+    4 Na  0.50000000000000  0.50000000000000  0.00000000000000  22.990
+    5 Cl  0.50000000000000  0.50000000000000  0.50000000000000  35.453
+    6 Cl  0.50000000000000  0.00000000000000  0.00000000000000  35.453
+    7 Cl  0.00000000000000  0.50000000000000  0.00000000000000  35.453
+    8 Cl  0.00000000000000  0.00000000000000  0.50000000000000  35.453
+----------------------------------------------------------------------------
+Supercell (dim): [2 2 2]
+Primitive matrix:
+  [0.  0.5 0.5]
+  [0.5 0.  0.5]
+  [0.5 0.5 0. ]
+Displacement distance: 0.03
+Number of displacements: 100
+NAC parameters were read from "BORN".
+Spacegroup: Fm-3m (225)
+Displacement dataset was written in "phono3py_disp.yaml".
+-------------------------[time 2024-09-19 14:40:00]-------------------------
+                 _
+   ___ _ __   __| |
+  / _ \ '_ \ / _` |
+ |  __/ | | | (_| |
+  \___|_| |_|\__,_|
+
+
+

For the generated supercells, forces and energies are calculated. Here it is +assumed to use the VASP code. Once the calculations are complete, the data +(forces and energies) can be extracted using the following command:

+
% phono3py --sp --cf3 vasprun_xmls/vasprun-{00001..00100}.xml
+
+
+

This command extracts the necessary data and stores it in the +phono3py_params.yaml file. For more details, refer to the description of the +–sp option. Currently, supercell energy extraction from +calculator outputs is only supported when using the VASP interface.

+
+

Note

+

A set of the VASP calculation results is placed in example/NaCl-rd. It is +obtained by

+
% tar xvfa ../NaCl-rd/vasprun_xmls.tar.xz
+
+
+
+
+
+

Steps 4-7: Force constants calculation (systematic displacements in step 5)#

+

After developing MLPs, displacements are generated systematically considering +crystal symmetry.

+

Having phono3py_params.yaml, phono3py is executed with --pypolymlp option,

+
% phono3py-load --pypolymlp phono3py_params.yaml
+        _                      _____
+  _ __ | |__   ___  _ __   ___|___ / _ __  _   _
+ | '_ \| '_ \ / _ \| '_ \ / _ \ |_ \| '_ \| | | |
+ | |_) | | | | (_) | | | | (_) |__) | |_) | |_| |
+ | .__/|_| |_|\___/|_| |_|\___/____/| .__/ \__, |
+ |_|                                |_|    |___/
+                                           3.5.0
+
+-------------------------[time 2024-09-19 15:20:27]-------------------------
+Compiled with OpenMP support (max 10 threads).
+Running in phono3py.load mode.
+Python version 3.12.6
+Spglib version 2.5.0
+----------------------------- General settings -----------------------------
+HDF5 data compression filter: gzip
+Crystal structure was read from "phono3py_params.yaml".
+Supercell (dim): [2 2 2]
+Primitive matrix:
+  [0.  0.5 0.5]
+  [0.5 0.  0.5]
+  [0.5 0.5 0. ]
+Spacegroup: Fm-3m (225)
+Use -v option to watch primitive cell, unit cell, and supercell structures.
+NAC parameters were read from "phono3py_params.yaml".
+----------------------------- Force constants ------------------------------
+Displacement dataset for fc3 was read from "phono3py_params.yaml".
+----------------------------- pypolymlp start ------------------------------
+Pypolymlp is a generator of polynomial machine learning potentials.
+Please cite the paper: A. Seko, J. Appl. Phys. 133, 011101 (2023).
+Pypolymlp is developed at https://github.com/sekocha/pypolymlp.
+Developing MLPs by pypolymlp...
+Regression: cholesky decomposition ...
+- alpha: 0.001
+- alpha: 0.01
+- alpha: 0.1
+- alpha: 1.0
+- alpha: 10.0
+Clear training X.T @ X
+Calculate X.T @ X for test data
+Clear test X.T @ X
+Regression: model selection ...
+- alpha = 1.000e-03 : rmse (train, test) = 9.39542e+14 9.39543e+14
+- alpha = 1.000e-02 : rmse (train, test) = 9.39542e+14 9.39543e+14
+- alpha = 1.000e-01 : rmse (train, test) = 0.03738 0.04961
+- alpha = 1.000e+00 : rmse (train, test) = 0.03900 0.04742
+- alpha = 1.000e+01 : rmse (train, test) = 0.04058 0.04584
+MLPs were written into "phono3py.pmlp"
+------------------------------ pypolymlp end -------------------------------
+Generate displacements
+  Displacement distance: 0.001
+Evaluate forces in 292 supercells by pypolymlp
+Computing fc3[ 1, x, x ] using numpy.linalg.pinv.
+Displacements (in Angstrom):
+    [ 0.0010  0.0000  0.0000]
+    [-0.0010  0.0000  0.0000]
+Computing fc3[ 33, x, x ] using numpy.linalg.pinv.
+Displacements (in Angstrom):
+    [ 0.0010  0.0000  0.0000]
+    [-0.0010  0.0000  0.0000]
+Expanding fc3.
+fc3 was symmetrized.
+fc2 was symmetrized.
+Max drift of fc3: -0.000000 (zzz) -0.000000 (zzz) -0.000000 (zzz)
+Max drift of fc2: -0.000000 (zz) -0.000000 (zz)
+fc3 was written into "fc3.hdf5".
+fc2 was written into "fc2.hdf5".
+----------- None of ph-ph interaction calculation was performed. -----------
+Dataset generated using MMLPs was written in "phono3py_mlp_eval_dataset.yaml".
+Summary of calculation was written in "phono3py.yaml".
+-------------------------[time 2024-09-19 15:21:41]-------------------------
+                 _
+   ___ _ __   __| |
+  / _ \ '_ \ / _` |
+ |  __/ | | | (_| |
+  \___|_| |_|\__,_|
+
+
+

Information about the development of MLPs using pypolymlp is provided between +the pypolymlp start and pypolymlp end sections. The polynomial MLPs are +saved in the phono3py.pmlp file, which can be reused in subsequent phono3py +executions with the --pypolymlp option when only displacements (and no forces) +are provided.

+

After the MLPs are developed, systematic displacements, such as those involving +the displacement of one or two atoms in supercells, are generated with a +displacement distance of 0.001 Angstrom. The forces for these supercells are +then evaluated using pypolymlp. Both the generated displacements and the +corresponding forces are stored in the phono3py_mlp_eval_dataset file.

+
+
+

Steps 4-6: Force constants calculation (random displacements in step 5)#

+

After developing MLPs, random displacements are generated by specifying +–rd option. To compute force constants +with random displacements, an external force constants calculator is necessary. +For this, symfc is used which is invoked by --symfc option.

+

Having phono3py_params.yaml, phono3py is executed with --pypolymlp option,

+
% phono3py-load --pypolymlp --rd 200 --symfc phono3py_params.yaml
+        _                      _____
+  _ __ | |__   ___  _ __   ___|___ / _ __  _   _
+ | '_ \| '_ \ / _ \| '_ \ / _ \ |_ \| '_ \| | | |
+ | |_) | | | | (_) | | | | (_) |__) | |_) | |_| |
+ | .__/|_| |_|\___/|_| |_|\___/____/| .__/ \__, |
+ |_|                                |_|    |___/
+                       3.5.0-dev22+g575c4107
+
+-------------------------[time 2024-09-19 15:33:23]-------------------------
+Compiled with OpenMP support (max 10 threads).
+Running in phono3py.load mode.
+Python version 3.12.6
+Spglib version 2.5.0
+----------------------------- General settings -----------------------------
+HDF5 data compression filter: gzip
+Crystal structure was read from "phono3py_params.yaml".
+Supercell (dim): [2 2 2]
+Primitive matrix:
+  [0.  0.5 0.5]
+  [0.5 0.  0.5]
+  [0.5 0.5 0. ]
+Spacegroup: Fm-3m (225)
+Use -v option to watch primitive cell, unit cell, and supercell structures.
+NAC parameters were read from "phono3py_params.yaml".
+----------------------------- Force constants ------------------------------
+Displacement dataset for fc3 was read from "phono3py_params.yaml".
+----------------------------- pypolymlp start ------------------------------
+Pypolymlp is a generator of polynomial machine learning potentials.
+Please cite the paper: A. Seko, J. Appl. Phys. 133, 011101 (2023).
+Pypolymlp is developed at https://github.com/sekocha/pypolymlp.
+Developing MLPs by pypolymlp...
+Regression: cholesky decomposition ...
+- alpha: 0.001
+- alpha: 0.01
+- alpha: 0.1
+- alpha: 1.0
+- alpha: 10.0
+Clear training X.T @ X
+Calculate X.T @ X for test data
+Clear test X.T @ X
+Regression: model selection ...
+- alpha = 1.000e-03 : rmse (train, test) = 9.39542e+14 9.39543e+14
+- alpha = 1.000e-02 : rmse (train, test) = 9.39542e+14 9.39543e+14
+- alpha = 1.000e-01 : rmse (train, test) = 0.03738 0.04961
+- alpha = 1.000e+00 : rmse (train, test) = 0.03900 0.04742
+- alpha = 1.000e+01 : rmse (train, test) = 0.04058 0.04584
+MLPs were written into "phono3py.pmlp"
+------------------------------ pypolymlp end -------------------------------
+Generate random displacements
+  Twice of number of snapshots will be generated for plus-minus displacements.
+  Displacement distance: 0.001
+Evaluate forces in 400 supercells by pypolymlp
+-------------------------------- Symfc start -------------------------------
+Symfc is a non-trivial force constants calculator. Please cite the paper:
+A. Seko and A. Togo, arXiv:2403.03588.
+Symfc is developed at https://github.com/symfc/symfc.
+Computing [2, 3] order force constants.
+Increase log-level to watch detailed symfc log.
+--------------------------------- Symfc end --------------------------------
+-------------------------------- Symfc start -------------------------------
+Symfc is a non-trivial force constants calculator. Please cite the paper:
+A. Seko and A. Togo, arXiv:2403.03588.
+Symfc is developed at https://github.com/symfc/symfc.
+Computing [2] order force constants.
+Increase log-level to watch detailed symfc log.
+--------------------------------- Symfc end --------------------------------
+Max drift of fc3: -0.000000 (xyx) 0.000000 (zyy) -0.000000 (xyx)
+Max drift of fc2: 0.000000 (xx) 0.000000 (xx)
+fc3 was written into "fc3.hdf5".
+fc2 was written into "fc2.hdf5".
+----------- None of ph-ph interaction calculation was performed. -----------
+Dataset generated using MMLPs was written in "phono3py_mlp_eval_dataset.yaml".
+Summary of calculation was written in "phono3py.yaml".
+-------------------------[time 2024-09-19 15:34:41]-------------------------
+                 _
+   ___ _ __   __| |
+  / _ \ '_ \ / _` |
+ |  __/ | | | (_| |
+  \___|_| |_|\__,_|
+
+
+

The development of MLPs follows the same procedure as described for the +systematic displacements (in step 5) above.

+

After the MLPs are developed, 200 supercells with random directional +displacements are generated. These displacements are then inverted, resulting in +an additional 200 supercells. In total, 400 supercells are created. The forces +for these supercells are then evaluated. Finally, the force constants are +calculated using symfc.

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+ + © Copyright 2015, Atsushi Togo. +
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