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optimiz-rs/examples/notebooks/14_mckean_vlasov.ipynb
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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

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{
"cells": [
{
"cell_type": "markdown",
"id": "d5d7832e",
"metadata": {},
"source": [
"# 14 — McKeanVlasov mean-reverting dynamics"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "f097c046",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-12T10:16:13.179893Z",
"iopub.status.busy": "2026-05-12T10:16:13.179607Z",
"iopub.status.idle": "2026-05-12T10:16:13.884485Z",
"shell.execute_reply": "2026-05-12T10:16:13.882300Z"
}
},
"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": "code",
"execution_count": 2,
"id": "3131411f",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-12T10:16:13.888394Z",
"iopub.status.busy": "2026-05-12T10:16:13.888018Z",
"iopub.status.idle": "2026-05-12T10:16:13.982143Z",
"shell.execute_reply": "2026-05-12T10:16:13.980768Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"initial mean = 7.105427357601002e-17\n",
"final mean = -0.003086441510327802\n",
"final std = 0.43383156366774833\n"
]
}
],
"source": [
"init = np.linspace(-2.0, 2.0, 200).tolist()\n",
"init_mean = float(np.mean(init))\n",
"res = opt.mean_reverting_mckean_vlasov(\n",
" initial=init, theta=1.0, sigma=0.1,\n",
" n_steps=1000, t_horizon=1.0, seed=42,\n",
")\n",
"n_t = res['n_steps']; n_p = res['n_particles']\n",
"X = np.array(res['paths_flat']).reshape(n_t, n_p)\n",
"tg = np.array(res['time_grid'])\n",
"print('initial mean =', init_mean)\n",
"print('final mean =', float(X[-1].mean()))\n",
"print('final std =', float(X[-1].std()))\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "584c7508",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-12T10:16:13.986355Z",
"iopub.status.busy": "2026-05-12T10:16:13.985990Z",
"iopub.status.idle": "2026-05-12T10:16:14.374960Z",
"shell.execute_reply": "2026-05-12T10:16:14.373158Z"
}
},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 770x440 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"ax.plot(tg, X[:, ::20], color='tab:blue', alpha=0.2, lw=0.6)\n",
"ax.plot(tg, X.mean(axis=1), color='red', lw=2, label='empirical mean')\n",
"ax.axhline(init_mean, color='k', ls=':', label='initial mean')\n",
"ax.set_xlabel('t'); ax.set_ylabel('X^i_t'); ax.legend(); ax.grid(alpha=0.3)\n",
"ax.set_title('Mean-reverting McKeanVlasov — 200 particles')\n",
"fig.tight_layout(); plt.show()\n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "f2c35644",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-12T10:16:14.379071Z",
"iopub.status.busy": "2026-05-12T10:16:14.378605Z",
"iopub.status.idle": "2026-05-12T10:16:14.946058Z",
"shell.execute_reply": "2026-05-12T10:16:14.944401Z"
}
},
"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",
"ax.hist(X[0], bins=30, alpha=0.5, label='t = 0', density=True)\n",
"ax.hist(X[-1], bins=30, alpha=0.5, label='t = T', density=True)\n",
"ax.set_xlabel('x'); ax.set_ylabel('empirical density'); ax.legend(); ax.grid(alpha=0.3)\n",
"ax.set_title('Marginal density at t = 0 and t = T')\n",
"fig.tight_layout(); plt.show()\n"
]
},
{
"cell_type": "markdown",
"id": "4e622c9b",
"metadata": {},
"source": [
"**Verified:** empirical mean stays within `0.05` of the initial mean."
]
}
],
"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
}