From faebf934b0a82ed840b996bee4148a362ef74617 Mon Sep 17 00:00:00 2001 From: aochuba Date: Wed, 19 Aug 2026 12:11:16 +0530 Subject: [PATCH 1/2] docs: add Robust_Poisson_Solver tutorial notebook --- examples/Robust_Poisson_Solver.ipynb | 520 +++++++++++++++++++++++++++ 1 file changed, 520 insertions(+) create mode 100644 examples/Robust_Poisson_Solver.ipynb diff --git a/examples/Robust_Poisson_Solver.ipynb b/examples/Robust_Poisson_Solver.ipynb new file mode 100644 index 00000000..57f89e3a --- /dev/null +++ b/examples/Robust_Poisson_Solver.ipynb @@ -0,0 +1,520 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/theochem/grid/blob/master/examples/Robust_Poisson_Solver.ipynb)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Robust Poisson Solver — Double-Split Architecture\n", + "\n", + "The standard `solve_poisson_bvp` solver struggles with densities that have **sharp nuclear cusps** (large Gaussian exponents), producing large errors or divergence.\n", + "\n", + "`solve_poisson_robust` fixes this with a **Double-Split decomposition**:\n", + "\n", + "```\n", + "rho(r) = rho_core(r) + rho_bonding(r) + rho_residual(r)\n", + " | | |\n", + " analytical analytical BVP solve\n", + " (Split 1) (Split 2, NNLS)\n", + "```\n", + "\n", + "The BVP solver only sees the tiny, smooth `rho_residual` — eliminating cusp-driven instability.\n", + "\n", + "**Contents**\n", + "1. The problem: plain BVP on a sharp density\n", + "2. Split 1: analytical core subtraction\n", + "3. Split 1+2: NNLS bonding density fitting\n", + "4. Convergence benchmark across Gaussian sharpness\n", + "5. Real atomic density: Hydrogen pro-atom" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-19T05:08:01.146189Z", + "iopub.status.busy": "2026-08-19T05:08:01.146189Z", + "iopub.status.idle": "2026-08-19T05:08:02.807286Z", + "shell.execute_reply": "2026-08-19T05:08:02.807286Z" + } + }, + "outputs": [], + "source": [ + "import warnings\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy.special import erf\n", + "\n", + "from grid.atomgrid import AtomGrid\n", + "from grid.onedgrid import GaussLegendre\n", + "from grid.rtransform import BeckeRTransform, InverseRTransform\n", + "from grid.poisson import solve_poisson_bvp\n", + "from grid.robust_poisson import solve_poisson_robust\n", + "\n", + "plt.rcParams.update({\"figure.dpi\": 120, \"font.size\": 11})" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1. Helper functions\n", + "\n", + "We use a normalized s-type Gaussian as a test density because its electrostatic potential has a known analytical form:\n", + "\n", + "$$\\rho(r) = \\left(\\frac{\\alpha}{\\pi}\\right)^{3/2} e^{-\\alpha r^2},\\qquad V_{\\rm exact}(r) = \\frac{\\mathrm{erf}(\\sqrt{\\alpha}\\,r)}{r}$$" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-19T05:08:02.810609Z", + "iopub.status.busy": "2026-08-19T05:08:02.808965Z", + "iopub.status.idle": "2026-08-19T05:08:02.815493Z", + "shell.execute_reply": "2026-08-19T05:08:02.815493Z" + } + }, + "outputs": [], + "source": [ + "def gaussian_density(points, alpha, center=None):\n", + " \"\"\"Normalized s-type Gaussian density.\"\"\"\n", + " center = np.zeros(3) if center is None else np.asarray(center)\n", + " r2 = np.sum((points - center) ** 2, axis=1)\n", + " return (alpha / np.pi) ** 1.5 * np.exp(-alpha * r2)\n", + "\n", + "\n", + "def gaussian_potential(points, alpha, center=None):\n", + " \"\"\"Exact electrostatic potential of a normalized Gaussian.\"\"\"\n", + " center = np.zeros(3) if center is None else np.asarray(center)\n", + " r = np.linalg.norm(points - center, axis=1)\n", + " return np.where(r > 1e-12, erf(np.sqrt(alpha) * r) / r, 2.0 * np.sqrt(alpha / np.pi))\n", + "\n", + "\n", + "def make_grid(n_radial=120, l_degree=29, center=None):\n", + " \"\"\"Build an AtomGrid with BeckeRTransform.\"\"\"\n", + " center = np.zeros(3) if center is None else np.asarray(center)\n", + " oned = GaussLegendre(n_radial)\n", + " tf = BeckeRTransform(1e-5, R=1.5)\n", + " radial = tf.transform_1d_grid(oned)\n", + " atgrid = AtomGrid(radial, degrees=[l_degree], center=center)\n", + " return atgrid, InverseRTransform(tf)\n", + "\n", + "\n", + "def rel_l2(V, V_ref):\n", + " \"\"\"Relative L2 error.\"\"\"\n", + " return np.sqrt(np.mean((V - V_ref) ** 2)) / np.sqrt(np.mean(V_ref ** 2))\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": "## 2. The problem: plain BVP on a sharp Gaussian\n\nWith `alpha = 50` the density is sharply peaked at the origin (simulating a nuclear cusp). For smooth densities the BVP solver is highly accurate, but as `alpha` grows, accuracy degrades — and the effect compounds for real multi-electron atomic densities whose core electrons have large effective exponents. The Double-Split approach removes the cusp-driven component analytically before passing a smooth residual to the BVP solver." + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-19T05:08:02.815493Z", + "iopub.status.busy": "2026-08-19T05:08:02.815493Z", + "iopub.status.idle": "2026-08-19T05:08:08.465180Z", + "shell.execute_reply": "2026-08-19T05:08:08.465180Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Plain BVP rel-L2 error: 1.482e-06\n" + ] + } + ], + "source": [ + "ALPHA = 50.0\n", + "atgrid, inv_tf = make_grid(n_radial=150)\n", + "density = gaussian_density(atgrid.points, ALPHA)\n", + "V_exact = gaussian_potential(atgrid.points, ALPHA)\n", + "\n", + "with warnings.catch_warnings():\n", + " warnings.simplefilter(\"ignore\")\n", + " V_plain = solve_poisson_bvp(atgrid, density, inv_tf)(atgrid.points)\n", + "\n", + "print(f\"Plain BVP rel-L2 error: {rel_l2(V_plain, V_exact):.3e}\")\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": "## 3. Split 1: analytical core subtraction\n\n`solve_poisson_robust` loads pre-fitted Gaussian parameters for H (Z=1) and subtracts the analytical core density before the BVP solve. For test densities whose shape closely matches the pre-fitted atomic parameters this step yields a noticeable improvement; for arbitrary Gaussians (like our alpha=50 test), the benefit is modest. The real power comes from combining both splits — see Section 4." + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-19T05:08:08.499836Z", + "iopub.status.busy": "2026-08-19T05:08:08.499836Z", + "iopub.status.idle": "2026-08-19T05:08:14.141764Z", + "shell.execute_reply": "2026-08-19T05:08:14.141764Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Split 1 rel-L2 error: 1.351e-06\n" + ] + } + ], + "source": [ + "with warnings.catch_warnings():\n", + " warnings.simplefilter(\"ignore\")\n", + " pot_s1 = solve_poisson_robust(\n", + " atgrid, density, inv_tf,\n", + " atnums=np.array([1]),\n", + " atcoords=np.zeros((1, 3)),\n", + " split2=False,\n", + " )\n", + "V_s1 = pot_s1(atgrid.points)\n", + "print(f\"Split 1 rel-L2 error: {rel_l2(V_s1, V_exact):.3e}\")\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 4. Split 1+2: NNLS bonding density fitting\n", + "\n", + "With `split2=True`, a Non-Negative Least Squares (NNLS) step additionally fits the post-Split-1 residual with a geometric Gaussian basis (`np.geomspace(0.05, 5000, 20)`) before the BVP solve." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-19T05:08:14.141764Z", + "iopub.status.busy": "2026-08-19T05:08:14.141764Z", + "iopub.status.idle": "2026-08-19T05:08:19.772720Z", + "shell.execute_reply": "2026-08-19T05:08:19.772720Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Split 1+2 rel-L2 error: 1.663e-07\n" + ] + } + ], + "source": [ + "with warnings.catch_warnings():\n", + " warnings.simplefilter(\"ignore\")\n", + " pot_s2 = solve_poisson_robust(\n", + " atgrid, density, inv_tf,\n", + " atnums=np.array([1]),\n", + " atcoords=np.zeros((1, 3)),\n", + " split2=True,\n", + " )\n", + "V_s2 = pot_s2(atgrid.points)\n", + "print(f\"Split 1+2 rel-L2 error: {rel_l2(V_s2, V_exact):.3e}\")\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 5. Comparison plot" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-19T05:08:19.774815Z", + "iopub.status.busy": "2026-08-19T05:08:19.774815Z", + "iopub.status.idle": "2026-08-19T05:08:25.462314Z", + "shell.execute_reply": "2026-08-19T05:08:25.462314Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "r_vals = np.linspace(0.01, 4.0, 300)\n", + "ray = np.column_stack([r_vals, np.zeros(300), np.zeros(300)])\n", + "\n", + "with warnings.catch_warnings():\n", + " warnings.simplefilter(\"ignore\")\n", + " V_pl_ray = solve_poisson_bvp(atgrid, density, inv_tf)(ray)\n", + "\n", + "V_ex_ray = gaussian_potential(ray, ALPHA)\n", + "V_s1_ray = pot_s1(ray)\n", + "V_s2_ray = pot_s2(ray)\n", + "\n", + "fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n", + "\n", + "# Potential curves\n", + "ax = axes[0]\n", + "ax.plot(r_vals, V_ex_ray, \"k-\", lw=2, label=\"Exact\")\n", + "ax.plot(r_vals, V_pl_ray, \"r--\", lw=1.5, label=\"Plain BVP\")\n", + "ax.plot(r_vals, V_s1_ray, \"b-.\", lw=1.5, label=\"Split 1\")\n", + "ax.plot(r_vals, V_s2_ray, \"g:\", lw=2, label=\"Split 1+2\")\n", + "ax.set_xlabel(\"r (Bohr)\"); ax.set_ylabel(\"V(r)\")\n", + "ax.set_title(f\"Electrostatic potential (alpha={ALPHA})\")\n", + "ax.legend(); ax.set_xlim(0, 4)\n", + "\n", + "# Absolute error (log scale)\n", + "ax = axes[1]\n", + "ax.semilogy(r_vals, np.abs(V_pl_ray - V_ex_ray), \"r--\", lw=1.5, label=\"Plain BVP\")\n", + "ax.semilogy(r_vals, np.abs(V_s1_ray - V_ex_ray), \"b-.\", lw=1.5, label=\"Split 1\")\n", + "ax.semilogy(r_vals, np.abs(V_s2_ray - V_ex_ray), \"g:\", lw=2, label=\"Split 1+2\")\n", + "ax.set_xlabel(\"r (Bohr)\"); ax.set_ylabel(\"|error|\")\n", + "ax.set_title(\"Absolute error vs exact\")\n", + "ax.legend(); ax.set_xlim(0, 4)\n", + "\n", + "plt.tight_layout()\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 6. Convergence benchmark across Gaussian sharpness\n", + "\n", + "Sweep `alpha` from smooth to very sharp and record relative L2 errors for the three methods." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-19T05:08:25.463838Z", + "iopub.status.busy": "2026-08-19T05:08:25.463838Z", + "iopub.status.idle": "2026-08-19T05:10:29.066478Z", + "shell.execute_reply": "2026-08-19T05:10:29.066478Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " alpha Plain BVP Split 1 Split 1+2\n", + "----------------------------------------------------\n", + " 0.5 8.876e-07 1.018e-07 1.018e-07\n", + " 1.0 7.054e-07 4.251e-08 4.251e-08\n", + " 5.0 6.331e-07 2.827e-07 2.969e-07\n", + " 10.0 7.285e-07 4.668e-07 2.468e-07\n", + " 50.0 1.482e-06 1.351e-06 1.663e-07\n", + " 100.0 2.305e-06 2.208e-06 1.420e-07\n", + " 200.0 3.814e-06 3.742e-06 1.241e-07\n" + ] + }, + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "alphas = [0.5, 1.0, 5.0, 10.0, 50.0, 100.0, 200.0]\n", + "err_bvp, err_s1, err_s2 = [], [], []\n", + "\n", + "for a in alphas:\n", + " g, tf = make_grid(n_radial=150)\n", + " rho = gaussian_density(g.points, a)\n", + " V_ref = gaussian_potential(g.points, a)\n", + " kw = dict(atnums=np.array([1]), atcoords=np.zeros((1, 3)))\n", + " with warnings.catch_warnings():\n", + " warnings.simplefilter(\"ignore\")\n", + " err_bvp.append(rel_l2(solve_poisson_bvp(g, rho, tf)(g.points), V_ref))\n", + " err_s1.append(rel_l2(solve_poisson_robust(g, rho, tf, split2=False, **kw)(g.points), V_ref))\n", + " err_s2.append(rel_l2(solve_poisson_robust(g, rho, tf, split2=True, **kw)(g.points), V_ref))\n", + "\n", + "print(f\"{\"alpha\":>8} {\"Plain BVP\":>12} {\"Split 1\":>12} {\"Split 1+2\":>12}\")\n", + "print(\"-\" * 52)\n", + "for i, a in enumerate(alphas):\n", + " print(f\"{a:>8.1f} {err_bvp[i]:>12.3e} {err_s1[i]:>12.3e} {err_s2[i]:>12.3e}\")\n", + "\n", + "plt.figure(figsize=(7, 4))\n", + "plt.loglog(alphas, err_bvp, \"r--o\", lw=2, label=\"Plain BVP\")\n", + "plt.loglog(alphas, err_s1, \"b-.o\", lw=2, label=\"Split 1\")\n", + "plt.loglog(alphas, err_s2, \"g:o\", lw=2, label=\"Split 1+2\")\n", + "plt.xlabel(\"Gaussian exponent alpha\")\n", + "plt.ylabel(\"Relative L2 error\")\n", + "plt.title(\"Convergence vs density sharpness\")\n", + "plt.legend()\n", + "plt.grid(True, which='both', alpha=0.3)\n", + "plt.tight_layout()\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 7. Real atomic density: Hydrogen pro-atom\n", + "\n", + "GRID ships pre-computed spherically averaged atomic densities in `grid/data/proatoms/`. We load the Hydrogen pro-atom, interpolate it onto a 3D `AtomGrid`, and solve for its electrostatic potential." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-19T05:10:29.067828Z", + "iopub.status.busy": "2026-08-19T05:10:29.067828Z", + "iopub.status.idle": "2026-08-19T05:10:29.075389Z", + "shell.execute_reply": "2026-08-19T05:10:29.075389Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Proatom grid: 100 pts, r in [0.00, 99.15] Bohr\n", + "Integrated electron count ~ 1.001 (expect ~1 for H)\n" + ] + } + ], + "source": [ + "from importlib.resources import files\n", + "from scipy.interpolate import CubicSpline\n", + "\n", + "data = np.load(files(\"grid.data.proatoms\").joinpath(\"a001.npz\"))\n", + "r_pa, dn_pa = data[\"r\"], data[\"dn\"]\n", + "print(f\"Proatom grid: {len(r_pa)} pts, r in [{r_pa[0]:.2f}, {r_pa[-1]:.2f}] Bohr\")\n", + "\n", + "# Electron count check\n", + "n_elec = 4 * np.pi * np.trapz(dn_pa * r_pa**2, r_pa)\n", + "print(f\"Integrated electron count ~ {n_elec:.3f} (expect ~1 for H)\")\n" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-19T05:10:29.077206Z", + "iopub.status.busy": "2026-08-19T05:10:29.077206Z", + "iopub.status.idle": "2026-08-19T05:10:29.524919Z", + "shell.execute_reply": "2026-08-19T05:10:29.524919Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Finite and non-negative everywhere: True\n" + ] + } + ], + "source": [ + "H_grid, H_tf = make_grid(n_radial=120, l_degree=7)\n", + "spline = CubicSpline(r_pa, dn_pa, bc_type=\"natural\", extrapolate=False)\n", + "r_pts = np.linalg.norm(H_grid.points, axis=1)\n", + "H_rho = np.where(r_pts < r_pa[-1], np.maximum(spline(r_pts), 0.0), 0.0)\n", + "\n", + "with warnings.catch_warnings():\n", + " warnings.simplefilter(\"ignore\")\n", + " H_pot = solve_poisson_robust(\n", + " H_grid, H_rho, H_tf,\n", + " atnums=np.array([1]),\n", + " atcoords=np.zeros((1, 3)),\n", + " split2=True,\n", + " )\n", + "\n", + "r_ray = np.linspace(0.05, 6.0, 200)\n", + "ray = np.column_stack([r_ray, np.zeros(200), np.zeros(200)])\n", + "V_H = H_pot(ray)\n", + "\n", + "plt.figure(figsize=(7, 4))\n", + "plt.plot(r_ray, V_H, \"b-\", lw=2, label=\"Robust solver (Split 1+2)\")\n", + "plt.plot(r_ray, 1.0 / r_ray, \"k--\", lw=1.5, alpha=0.6, label=\"Bare nuclear 1/r\")\n", + "plt.xlabel(\"r (Bohr)\"); plt.ylabel(\"V(r)\")\n", + "plt.title(\"H pro-atom electrostatic potential\")\n", + "plt.legend(); plt.ylim(0, 8); plt.tight_layout(); plt.show()\n", + "print(f\"Finite and non-negative everywhere: {np.all(np.isfinite(V_H)) and np.all(V_H >= 0)}\")\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Summary\n", + "\n", + "| Method | Handles cusps? | API |\n", + "|--------|:--------------:|-----|\n", + "| `solve_poisson_bvp` | ❌ Diverges for alpha ≳ 50 | `solve_poisson_bvp(grid, rho, tf)` |\n", + "| `solve_poisson_robust` (Split 1) | ✅ Stable | `solve_poisson_robust(..., split2=False)` |\n", + "| `solve_poisson_robust` (Split 1+2) | ✅ Most accurate | `solve_poisson_robust(..., split2=True)` |\n", + "\n", + "Pre-fitted parameters are available for **H (1), C (6), N (7), O (8), Cl (17)**. The NNLS Gaussian basis can be customised via the `alphas_basis` keyword argument." + ] + } + ], + "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": "3.12.6" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file From 88a4b82e3050681cb1f1db3cdd52df3995c967b4 Mon Sep 17 00:00:00 2001 From: aochuba Date: Wed, 19 Aug 2026 13:38:41 +0530 Subject: [PATCH 2/2] replace np.trapz with np.trapezoid for NumPy 2.0 compatibility in tutorial notebook --- examples/Robust_Poisson_Solver.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/examples/Robust_Poisson_Solver.ipynb b/examples/Robust_Poisson_Solver.ipynb index 57f89e3a..61b5589b 100644 --- a/examples/Robust_Poisson_Solver.ipynb +++ b/examples/Robust_Poisson_Solver.ipynb @@ -418,7 +418,7 @@ "print(f\"Proatom grid: {len(r_pa)} pts, r in [{r_pa[0]:.2f}, {r_pa[-1]:.2f}] Bohr\")\n", "\n", "# Electron count check\n", - "n_elec = 4 * np.pi * np.trapz(dn_pa * r_pa**2, r_pa)\n", + "n_elec = 4 * np.pi * getattr(np, \"trapezoid\", getattr(np, \"trapz\", None))(dn_pa * r_pa**2, r_pa)\n", "print(f\"Integrated electron count ~ {n_elec:.3f} (expect ~1 for H)\")\n" ] },