Files
optimiz-rs/examples/notebooks/11_pde.ipynb
T
ThotDjehuty d8682f61e5 release(v2.0.0-alpha.2): PyO3 bindings + executed companion notebooks + Sphinx RST with inline plots
PyO3 abi3 bindings for the 13 v2.0.0 functions across 8 module groups:
  bsde, pde, stochastic_control, optimal_control::quadratic_impact_control,
  mean_field::mckean_vlasov, agent_based, inference, optimization.

8 executed companion notebooks under examples/notebooks/10_bsde.ipynb …
17_generative_calibration.ipynb (cell outputs and matplotlib figures
preserved as proof-of-work; verified against analytic ground truths).

8 Sphinx RST pages under docs/source/algorithms/{bsde,pde,stochastic_control,
quadratic_impact_control,mckean_vlasov,agent_based,robust_drift,
generative_calibration_hooks}.rst with .. math:: derivations and inline
.. image:: directives placed immediately after each .. code-block:: python
so each plot appears directly under the code that produced it.

18 PNG plot assets under docs/source/_static/v2/<group>/.

index.rst extended with a new 'v2.0 Generic Stochastic Control & PDE'
toctree caption.

Forbidden-vocabulary audit on new src/, docs/source/algorithms/ and
binding files: zero matches.

All previously stable APIs untouched; v2.0.0 is additive at the binding
level — no v1.x function signature was changed.
2026-05-12 12:18:14 +02:00

298 lines
188 KiB
Plaintext
Raw Blame History

This file contains ambiguous Unicode characters
This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.
{
"cells": [
{
"cell_type": "markdown",
"id": "5b95cdf9",
"metadata": {},
"source": [
"# 11 — PDE solvers\n",
"\n",
"FokkerPlanck, HJB, Poisson."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "f355a328",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-12T10:16:01.404135Z",
"iopub.status.busy": "2026-05-12T10:16:01.403772Z",
"iopub.status.idle": "2026-05-12T10:16:02.110007Z",
"shell.execute_reply": "2026-05-12T10:16:02.108701Z"
}
},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from optimizr import _core as opt\n",
"plt.rcParams['figure.figsize'] = (7, 4)\n",
"plt.rcParams['figure.dpi'] = 110\n"
]
},
{
"cell_type": "markdown",
"id": "7bd0f13d",
"metadata": {},
"source": [
"## Pure-diffusion FokkerPlanck\n",
"\n",
"$\\partial_t m = \\tfrac12 \\partial_{xx} m$ with Gaussian initial density should remain centred and approximately Gaussian."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "4199167d",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-12T10:16:02.113654Z",
"iopub.status.busy": "2026-05-12T10:16:02.113279Z",
"iopub.status.idle": "2026-05-12T10:16:02.515354Z",
"shell.execute_reply": "2026-05-12T10:16:02.513789Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"total mass at t=0: 1.0000000000000002\n",
"total mass at t=T: 0.9999999998667097\n",
"mean at t=T: -1.6653345369377348e-16\n"
]
}
],
"source": [
"res = opt.fokker_planck_constant(\n",
" mu=0.0, sigma_sq=1.0, init_sigma=1.0,\n",
" x_min=-8.0, x_max=8.0, n_x=401,\n",
" t_horizon=0.5, n_t=8000,\n",
")\n",
"x = np.array(res['x_grid'])\n",
"t = np.array(res['time_grid'])\n",
"nx = res['n_x']; nt = res['n_t']\n",
"M = np.array(res['density']).reshape(nt + 1, nx)\n",
"print('total mass at t=0:', np.trapezoid(M[0], x))\n",
"print('total mass at t=T:', np.trapezoid(M[-1], x))\n",
"print('mean at t=T:', np.trapezoid(x * M[-1], x))\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "ba80f3c4",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-12T10:16:02.519856Z",
"iopub.status.busy": "2026-05-12T10:16:02.519554Z",
"iopub.status.idle": "2026-05-12T10:16:02.912830Z",
"shell.execute_reply": "2026-05-12T10:16:02.911483Z"
}
},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 770x440 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"for k in [0, nt // 4, nt // 2, 3 * nt // 4, nt]:\n",
" ax.plot(x, M[k], label=f't = {t[k]:.2f}')\n",
"ax.set_xlim(-5, 5); ax.set_xlabel('x'); ax.set_ylabel('m(x, t)')\n",
"ax.set_title('Pure-diffusion FokkerPlanck'); ax.grid(alpha=0.3); ax.legend()\n",
"fig.tight_layout(); plt.show()\n"
]
},
{
"cell_type": "markdown",
"id": "1b2ef52c",
"metadata": {},
"source": [
"## 2-D Poisson eigenfunction\n",
"\n",
"$-\\Delta u = 2\\pi^2 \\sin(\\pi x)\\sin(\\pi y)$ on the unit square with zero Dirichlet boundary admits the exact solution $u(x,y) = \\sin(\\pi x)\\sin(\\pi y)$."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "1f2b19fb",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-12T10:16:02.916630Z",
"iopub.status.busy": "2026-05-12T10:16:02.915981Z",
"iopub.status.idle": "2026-05-12T10:16:03.039124Z",
"shell.execute_reply": "2026-05-12T10:16:03.037419Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"iterations = 690\n",
"residual = 9.865621268811964e-07\n",
"max error = 0.00013249923574043532\n"
]
}
],
"source": [
"n = 65\n",
"xs = np.linspace(0, 1, n); ys = np.linspace(0, 1, n)\n",
"X, Y = np.meshgrid(xs, ys, indexing='ij')\n",
"F = 2 * np.pi ** 2 * np.sin(np.pi * X) * np.sin(np.pi * Y)\n",
"res = opt.poisson_2d_zero_boundary(F.flatten().tolist(), n, n)\n",
"U = np.array(res['u']).reshape(n, n)\n",
"U_exact = np.sin(np.pi * X) * np.sin(np.pi * Y)\n",
"print('iterations =', res['iterations'])\n",
"print('residual =', res['residual'])\n",
"print('max error =', float(np.max(np.abs(U - U_exact))))\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "8ee99510",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-12T10:16:03.042379Z",
"iopub.status.busy": "2026-05-12T10:16:03.042041Z",
"iopub.status.idle": "2026-05-12T10:16:03.692138Z",
"shell.execute_reply": "2026-05-12T10:16:03.690583Z"
}
},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 1210x440 with 4 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, axes = plt.subplots(1, 2, figsize=(11, 4))\n",
"im0 = axes[0].imshow(U.T, origin='lower', extent=(0, 1, 0, 1), cmap='viridis')\n",
"axes[0].set_title('SOR solution'); plt.colorbar(im0, ax=axes[0])\n",
"im1 = axes[1].imshow((U - U_exact).T, origin='lower', extent=(0, 1, 0, 1), cmap='RdBu_r')\n",
"axes[1].set_title('error vs analytic'); plt.colorbar(im1, ax=axes[1])\n",
"fig.tight_layout(); plt.show()\n"
]
},
{
"cell_type": "markdown",
"id": "f3b99b10",
"metadata": {},
"source": [
"## 2-D HJB with quadratic terminal\n",
"\n",
"Heat-only relaxation ($H = 0$, σ² > 0) preserves a constant value, while a quadratic terminal $g(x) = ½(x²+y²)$ smooths."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "0cf4e23e",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-12T10:16:03.695325Z",
"iopub.status.busy": "2026-05-12T10:16:03.695038Z",
"iopub.status.idle": "2026-05-12T10:16:03.772635Z",
"shell.execute_reply": "2026-05-12T10:16:03.764763Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"V(0,0) = 0.018239022846662144\n",
"V(±1,±1) = 0.8159229411398733 0.8159229411398735\n"
]
}
],
"source": [
"res = opt.hjb_quadratic_2d(n_per_dim=21, x_min=-1.0, x_max=1.0,\n",
" n_t=200, t_horizon=0.2, sigma_sq=0.1)\n",
"ax_x = np.array(res['axis']); npd = res['n_per_dim']\n",
"V = np.array(res['value']).reshape(npd, npd)\n",
"print('V(0,0) =', V[npd // 2, npd // 2])\n",
"print('V(±1,±1) =', V[0, 0], V[-1, -1])\n"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "764c58ae",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-12T10:16:03.775694Z",
"iopub.status.busy": "2026-05-12T10:16:03.775402Z",
"iopub.status.idle": "2026-05-12T10:16:04.130581Z",
"shell.execute_reply": "2026-05-12T10:16:04.128409Z"
}
},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 770x440 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"im = ax.imshow(V.T, origin='lower', extent=(-1, 1, -1, 1), cmap='magma')\n",
"ax.set_title('HJB value V(0, x, y) — quadratic terminal')\n",
"plt.colorbar(im, ax=ax)\n",
"fig.tight_layout(); plt.show()\n"
]
},
{
"cell_type": "markdown",
"id": "3c13a863",
"metadata": {},
"source": [
"**Verified:** Poisson max-error vs analytic eigenfunction below `5e-3`; FokkerPlanck mean stays at 0 within `0.05`."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (rhftlab)",
"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": "3.11.13"
}
},
"nbformat": 4,
"nbformat_minor": 5
}