doc: upd with alabaster theme

doc/.buildinfo

@@ -0,0 +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: 838cceab9bf6970cab9bdd64855333e1
+tags: 645f666f9bcd5a90fca523b33c5a78b7

doc/_downloads/1d585bf137ffd9906e08a8ecc825a674/plot_1d.ipynb

@@ -15,7 +15,7 @@
       "cell_type": "markdown",
       "metadata": {},
       "source": [
-        "\n# 1D Poisson\n"
+        "\n# 1D Poisson\n\nThis example solves the Poisson equation in 1D\n\n\\begin{align}\\frac{\\partial^2 u}{\\partial x^2} = f\\end{align}\n\nwhere $f=\\frac{\\partial^2 u_\\mathrm{ref}}{\\partial x^2}$ and\n$u_\\mathrm{ref}$ is a reference solution.\n"
       ]
     },
     {
@@ -46,7 +46,7 @@
       "name": "python",
       "nbconvert_exporter": "python",
       "pygments_lexer": "ipython3",
-      "version": "3.8.10"
+      "version": "3.11.6"
     }
   },
   "nbformat": 4,

doc/_downloads/24eaf8dd253be2821d2f6eb64c3d9de4/fields.ipynb

@@ -15,7 +15,7 @@
       "cell_type": "markdown",
       "metadata": {},
       "source": [
-        "\n# field\n"
+        "\n# Field\n"
       ]
     },
     {
@@ -46,7 +46,7 @@
       "name": "python",
       "nbconvert_exporter": "python",
       "pygments_lexer": "ipython3",
-      "version": "3.8.10"
+      "version": "3.11.6"
     }
   },
   "nbformat": 4,

doc/_downloads/319ebb28fc2a00a84a4950112fc7bbca/infer_constant_adv.ipynb

@@ -46,7 +46,7 @@
       "name": "python",
       "nbconvert_exporter": "python",
       "pygments_lexer": "ipython3",
-      "version": "3.8.10"
+      "version": "3.11.6"
     }
   },
   "nbformat": 4,

doc/_downloads/42f8fd27774caacd783cf240e9bb5909/plot_1d.py

@@ -1,7 +1,15 @@
 #!/usr/bin/env python3
-"""
+r"""
 1D Poisson
 ==========
+
+This example solves the Poisson equation in 1D
+
+.. math::
+    \frac{\partial^2 u}{\partial x^2} = f
+
+where :math:`f=\frac{\partial^2 u_\mathrm{ref}}{\partial x^2}` and
+:math:`u_\mathrm{ref}` is a reference solution.
 """
 
 import odil

doc/_downloads/a059939c07979526d721d26d4ede54b1/fields.py

@@ -1,6 +1,6 @@
 #!/usr/bin/env python3
 """
-field
+Field
 =====
 """
 

doc/_downloads/ba280f66aff03682481a6b490d9023f6/poisson.ipynb

@@ -46,7 +46,7 @@
       "name": "python",
       "nbconvert_exporter": "python",
       "pygments_lexer": "ipython3",
-      "version": "3.8.10"
+      "version": "3.11.6"
     }
   },
   "nbformat": 4,

doc/_downloads/e2351dd27667554a422ac2d62b6aca00/harmonic_oscillator.py

@@ -0,0 +1,44 @@
+#!/usr/bin/env python3
+'''
+Harmonic oscillator
+===================
+'''
+
+
+import numpy as np
+import torch
+import torch.nn as nn
+import matplotlib.pyplot as plt
+import math
+
+def oscillator(d, w0, x):
+    w = math.sqrt(w0**2 - d**2)
+    phi = math.atan2(-d, w)
+    y = torch.exp(-d * x) * torch.cos(phi + w * x) / math.cos(phi)
+    return y
+
+
+torch.manual_seed(123)
+torch.set_default_dtype(torch.float32)
+d, w0 = 2.0, 20.0
+x = torch.linspace(0, 1, 500)[:, None]
+y = oscillator(d, w0, x)
+x_data = x[0:20:10]
+y_data = y[0:20:10]
+x_physics = torch.linspace(0, 1, 25)[:, None].requires_grad_(True)
+model = nn.Sequential(nn.Linear(1, 16), nn.Tanh(), nn.Linear(16, 16), nn.Tanh(), nn.Linear(16, 1))
+optimizer = torch.optim.Adam(model.parameters(), lr=1e-2)
+ones = torch.ones_like(x_physics)
+for i in range(5000):
+    optimizer.zero_grad()
+    yhp = model(x_physics)
+    dx, = torch.autograd.grad(yhp, x_physics, ones, create_graph=True)
+    dx2, = torch.autograd.grad(dx, x_physics, ones, create_graph=True)
+    physics = dx2 + 2 * d * dx + w0 * w0 * yhp
+    loss = torch.mean(
+        (model(x_data) - y_data)**2) + 1e-4 * torch.mean(physics**2)
+    loss.backward()
+    optimizer.step()
+plt.plot(x, y)
+plt.plot(x, model(x).detach(), '-')
+plt.show()

doc/_downloads/e30c667c9801d5417694b836d4b76169/harmonic_oscillator.ipynb

@@ -0,0 +1,54 @@
+{
+  "cells": [
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "%pip install -q git+https://github.com/cselab/odil"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "\n# Harmonic oscillator\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import numpy as np\nimport torch\nimport torch.nn as nn\nimport matplotlib.pyplot as plt\nimport math\n\ndef oscillator(d, w0, x):\n    w = math.sqrt(w0**2 - d**2)\n    phi = math.atan2(-d, w)\n    y = torch.exp(-d * x) * torch.cos(phi + w * x) / math.cos(phi)\n    return y\n\n\ntorch.manual_seed(123)\ntorch.set_default_dtype(torch.float32)\nd, w0 = 2.0, 20.0\nx = torch.linspace(0, 1, 500)[:, None]\ny = oscillator(d, w0, x)\nx_data = x[0:20:10]\ny_data = y[0:20:10]\nx_physics = torch.linspace(0, 1, 25)[:, None].requires_grad_(True)\nmodel = nn.Sequential(nn.Linear(1, 16), nn.Tanh(), nn.Linear(16, 16), nn.Tanh(), nn.Linear(16, 1))\noptimizer = torch.optim.Adam(model.parameters(), lr=1e-2)\nones = torch.ones_like(x_physics)\nfor i in range(5000):\n    optimizer.zero_grad()\n    yhp = model(x_physics)\n    dx, = torch.autograd.grad(yhp, x_physics, ones, create_graph=True)\n    dx2, = torch.autograd.grad(dx, x_physics, ones, create_graph=True)\n    physics = dx2 + 2 * d * dx + w0 * w0 * yhp\n    loss = torch.mean(\n        (model(x_data) - y_data)**2) + 1e-4 * torch.mean(physics**2)\n    loss.backward()\n    optimizer.step()\nplt.plot(x, y)\nplt.plot(x, model(x).detach(), '-')\nplt.show()"
+      ]
+    }
+  ],
+  "metadata": {
+    "kernelspec": {
+      "display_name": "Python 3",
+      "language": "python",
+      "name": "python3"
+    },
+    "language_info": {
+      "codemirror_mode": {
+        "name": "ipython",
+        "version": 3
+      },
+      "file_extension": ".py",
+      "mimetype": "text/x-python",
+      "name": "python",
+      "nbconvert_exporter": "python",
+      "pygments_lexer": "ipython3",
+      "version": "3.11.6"
+    }
+  },
+  "nbformat": 4,
+  "nbformat_minor": 0
+}