Add laplace FEM solution

Signed-off-by: Tom Freudenberg <[email protected]>

examples/new_examples/Exercise_1.ipynb

@@ -251,6 +251,38 @@
         "plot_sampler = tp.samplers.PlotSampler(plot_domain=omega, n_points=2000)\n",
         "fig = tp.utils.plot(model, lambda u : u, plot_sampler)"
       ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "And compare PINNs with the FEM-solution:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {},
+      "outputs": [],
+      "source": [
+        "import numpy as np\n",
+        "\n",
+        "# Get data from Github:\n",
+        "!wget https://github.com/TomF98/torchphysics/raw/main/examples/workshop/FEMData/LaplaceData/solution.npy\n",
+        "!wget https://github.com/TomF98/torchphysics/raw/main/examples/workshop/FEMData/LaplaceData/coordinates.npy\n",
+        "\n",
+        "# Read data:\n",
+        "coords = torch.tensor(np.load(\"coordinates.npy\"), dtype=torch.float32)\n",
+        "fem_sol = torch.tensor(np.load(\"solution.npy\"), dtype=torch.float32).reshape(-1, 1)\n",
+        "\n",
+        "# Evaluate Network:\n",
+        "model_out = model(tp.spaces.Points(coords, X)).as_tensor\n",
+        "\n",
+        "print(\"Difference to FEM in Sup-norm:\")\n",
+        "difference_sup = torch.max(torch.abs(fem_sol - model_out))\n",
+        "print(\"Absolute:\", difference_sup)\n",
+        "print(\"Relative:\", difference_sup / torch.max(torch.abs(fem_sol)))"
+      ]
     }
   ],
   "metadata": {