{ "cells": [ { "cell_type": "markdown", "id": "2b0a6d3c", "metadata": {}, "source": [ "# 5 · Solving the Minimization: Newton vs. Gradient Descent\n", "\n", "Time to open the solver box. We pin a beam's left edge, drag its **whole right edge**\n", "toward a target down and to the right, and drive the beam to equilibrium from rest with\n", "two methods that differ only in their search direction, **gradient descent** and\n", "**Newton**. Per iteration we track the energy, the gradient norm\n", "$\\lVert\\nabla E\\rVert$ and the **Newton decrement**\n", "$\\lambda = \\sqrt{\\nabla E^\\top H^{-1}\\nabla E}$.\n", "\n", "$$\\Delta x_{\\text{GD}} = -\\nabla E, \\qquad \\Delta x_{\\text{Newton}} = -H^{-1}\\nabla E.$$" ] }, { "cell_type": "markdown", "id": "f3fb652d", "metadata": {}, "source": [ "Imports, and every tunable parameter of this notebook." ] }, { "cell_type": "code", "execution_count": 1, "id": "c91153dc", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:26.037414Z", "iopub.status.busy": "2026-09-24T03:44:26.037235Z", "iopub.status.idle": "2026-09-24T03:44:26.610921Z", "shell.execute_reply": "2026-09-24T03:44:26.610326Z" } }, "outputs": [], "source": [ "%matplotlib inline\n", "import os\n", "import numpy as np\n", "import scipy as sp\n", "import matplotlib.pyplot as plt\n", "from matplotlib.colors import LogNorm\n", "import igl\n", "import simkit\n", "import utils\n", "\n", "NOTEBOOK = \"005_numerical_solver\" # this file's name\n", "RESULTS_DIR = utils.notebook_results_path(NOTEBOOK) # results/005_numerical_solver/\n", "MEDIA_DIR = \"media\" # tracked copies for the website\n", "# mesh\n", "NX, NY = 12, 4 # grid vertices along x and y\n", "WIDTH, HEIGHT = 2.0, 0.4 # beam size\n", "# material: a soft beam\n", "MATERIAL = \"macklin-mueller-neo-hookean\" # simkit elastic model (the old utils \"Neo-Hookean\")\n", "YM, PR = 0.5, 0.45 # Young's modulus, Poisson ratio\n", "# boundary conditions\n", "K_PIN = 1e2 # gentle pin spring on the left edge\n", "K_HANDLE = 25.0 # soft handle spring on the right edge\n", "HANDLE_OFFSET = np.array([0.5, -0.7]) # handle targets = rest right edge + this offset\n", "# solvers\n", "MAX_ITERS = 60 # iteration cap for both solvers\n", "TOL = 1e-9 # stop once the step ||alpha dx|| is smaller than this\n", "# finite-difference check\n", "FD_STEP = 1e-6 # central-difference step\n", "FD_NOISE = 0.05 # std of the random perturbation of the rest state\n", "SEED = 0 # RNG seed for that perturbation\n", "# visuals\n", "LIMS = ((-1.2, 1.8), (-1.3, 0.6)) # plot window around the beam and its targets\n", "FPS_NEWTON = 4 # one frame per Newton iteration\n", "FPS_GD = 10 # one frame per gradient-descent iteration\n", "PSI_RANGE = (1e-3, 3.0) # log color range of the energy-density plots" ] }, { "cell_type": "markdown", "id": "fddf622e", "metadata": {}, "source": [ "## The beam\n", "\n", "A $2\\times0.4$ beam from libigl's unit grid, with the constant operators the energy needs built\n", "once: the deformation Jacobian $J$ (each element's $F$ is a block of $Jx$), the per-element area\n", "and the per-element Lamé parameters. The left-edge vertices are pinned in place and the right-edge\n", "vertices form the handle, aimed at their rest positions shifted by `HANDLE_OFFSET`. The top panel\n", "marks pins (blue), handle (orange) and targets (×). The bottom panel shows the per-element\n", "area that weights each element's energy; it is uniform here and sums to the beam's area." ] }, { "cell_type": "code", "execution_count": 2, "id": "d21201aa", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:26.612705Z", "iopub.status.busy": "2026-09-24T03:44:26.612578Z", "iopub.status.idle": "2026-09-24T03:44:26.759886Z", "shell.execute_reply": "2026-09-24T03:44:26.759414Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "total area = 0.8000 (WIDTH * HEIGHT = 0.8000)\n" ] } ], "source": [ "V, T = igl.triangulated_grid(NX, NY) # unit square, NX x NY vertices\n", "X = (V - 0.5) * np.array([WIDTH, HEIGHT]) # centered WIDTH x HEIGHT beam\n", "n, dim = X.shape\n", "J = simkit.deformation_jacobian(X, T) # per-element F = (J @ x).reshape(-1, dim, dim)\n", "vol = simkit.volume(X, T) # per-element area\n", "mu, lam = simkit.ympr_to_lame(YM, PR)\n", "mu = np.full((len(T), 1), mu) # per-element Lame parameters\n", "lam = np.full((len(T), 1), lam)\n", "\n", "pin_idx = np.where(X[:, 0] <= X[:, 0].min() + 1e-6)[0]\n", "handle_idx = np.where(X[:, 0] >= X[:, 0].max() - 1e-6)[0]\n", "handle_targets = X[handle_idx] + HANDLE_OFFSET\n", "\n", "fig, axes = plt.subplots(2, 1, figsize=(7, 6.5))\n", "utils.plot_mesh(axes[0], X, T, pins=pin_idx, handles=handle_idx, lims=LIMS,\n", " title=f\"rest beam: {n} vertices, {len(T)} triangles\")\n", "axes[0].scatter(*handle_targets.T, marker=\"x\", s=60, linewidths=2, color=\"0.3\", zorder=6,\n", " label=\"target\")\n", "axes[0].legend(loc=\"upper right\", fontsize=8)\n", "utils.plot_scalar_field(axes[1], X, T, vol, vmin=0.0, vmax=1.2 * vol.max(),\n", " title=\"per-element area\", label=\"area\")\n", "fig.tight_layout()\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"mesh.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"005_mesh.png\"))\n", "plt.show()\n", "print(f\"total area = {vol.sum():.4f} (WIDTH * HEIGHT = {WIDTH * HEIGHT:.4f})\")" ] }, { "cell_type": "markdown", "id": "a80b1505", "metadata": {}, "source": [ "## The objective\n", "\n", "Elastic energy plus a gentle pin spring and a soft handle spring. The handle spring is kept\n", "**soft**, with forces of the same magnitude as the elastic ones, so the problem is not horribly\n", "ill-conditioned. With a stiff handle, gradient descent just yanks the handle and leaves the rest\n", "of the beam untouched.\n", "\n", "$$E(x) = E_{\\text{elastic}}(x) + \\tfrac{K_{\\text{pin}}}{2}\\lVert x_{\\text{pin}} - p\\rVert^2\n", " + \\tfrac{K_{\\text{handle}}}{2}\\lVert x_{\\text{handle}} - h\\rVert^2$$" ] }, { "cell_type": "code", "execution_count": 3, "id": "c920ae1a", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:26.761146Z", "iopub.status.busy": "2026-09-24T03:44:26.761053Z", "iopub.status.idle": "2026-09-24T03:44:26.764459Z", "shell.execute_reply": "2026-09-24T03:44:26.763855Z" } }, "outputs": [], "source": [ "def beam_system(X, J, vol, mu, lam, pin_idx, pin_targets, handle_idx, handle_targets):\n", " \"\"\"Neo-Hookean beam + soft pin + soft handle, in stacked vertex positions x.\"\"\"\n", " n, dim = X.shape\n", " Q_pin, b_pin = simkit.dirichlet_penalty(pin_idx, pin_targets, n, K_PIN)\n", " Q_handle, b_handle = simkit.dirichlet_penalty(handle_idx, handle_targets, n, K_HANDLE)\n", "\n", " def energy_func(x):\n", " E_elastic = simkit.energies.elastic_energy_x(x.reshape(n, dim), J, mu, lam, vol, MATERIAL)\n", " E_pin = simkit.energies.quadratic_energy(x, Q_pin, b_pin)\n", " E_handle = simkit.energies.quadratic_energy(x, Q_handle, b_handle)\n", " E_total = E_elastic + E_pin + E_handle\n", " return E_total\n", "\n", " def gradient_func(x):\n", " g_elastic = simkit.energies.elastic_gradient_x(x.reshape(n, dim), J, mu, lam, vol, MATERIAL)\n", " g_pin = simkit.energies.quadratic_gradient(x, Q_pin, b_pin)\n", " g_handle = simkit.energies.quadratic_gradient(x, Q_handle, b_handle)\n", " g_total = g_elastic + g_pin + g_handle\n", " return g_total\n", "\n", " def hessian_func(x):\n", " H_elastic = simkit.energies.elastic_hessian_x(x.reshape(n, dim), J, mu, lam, vol, MATERIAL, psd=True)\n", " H_pin = simkit.energies.quadratic_hessian(Q_pin)\n", " H_handle = simkit.energies.quadratic_hessian(Q_handle)\n", " H_total = H_elastic + H_pin + H_handle\n", " return H_total\n", "\n", " return energy_func, gradient_func, hessian_func" ] }, { "cell_type": "markdown", "id": "7e57af44", "metadata": {}, "source": [ "## The two solvers\n", "\n", "simkit's `newton_solver` and `gradient_descent` run the same loop: evaluate $g$ (and $H$), pick\n", "$\\Delta x$, choose a step $\\alpha$ by backtracking line search (tutorial 6), set\n", "$x \\leftarrow x + \\alpha\\Delta x$, and stop once $\\lVert\\alpha\\Delta x\\rVert <$ `TOL` or after\n", "`MAX_ITERS` steps. We run both from the rest state on the *same* objective with\n", "`return_info=True`, which records every step $(\\Delta x_k, \\alpha_k)$, and then recompute both\n", "first directions at $x_0$ by hand to confirm that the direction is the only difference." ] }, { "cell_type": "code", "execution_count": 4, "id": "c85ee762", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:26.765775Z", "iopub.status.busy": "2026-09-24T03:44:26.765684Z", "iopub.status.idle": "2026-09-24T03:44:26.798465Z", "shell.execute_reply": "2026-09-24T03:44:26.798077Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "first recorded step equals the hand-computed direction: gradient descent True, Newton True\n", "|dx_GD| = 43.0, |dx_Newton| = 3.6, angle between them = 62 deg\n" ] } ], "source": [ "energy_func, gradient_func, hessian_func = beam_system(X, J, vol, mu, lam, pin_idx, X[pin_idx],\n", " handle_idx, handle_targets)\n", "x0 = X.reshape(-1, 1).copy()\n", "_, newton_info = simkit.solvers.newton_solver(x0, energy_func, gradient_func, hessian_func,\n", " tolerance=TOL, max_iter=MAX_ITERS,\n", " do_line_search=True, return_info=True)\n", "_, gd_info = simkit.solvers.gradient_descent(x0, energy_func, gradient_func,\n", " tolerance=TOL, max_iter=MAX_ITERS,\n", " do_line_search=True, return_info=True)\n", "\n", "g0 = gradient_func(x0)\n", "dx_gd = -g0 # -grad E\n", "dx_newton = sp.sparse.linalg.spsolve(hessian_func(x0).tocsc(), -g0).reshape(-1, 1) # -H^-1 grad E\n", "cos_angle = (dx_gd.T @ dx_newton).item() / (np.linalg.norm(dx_gd) * np.linalg.norm(dx_newton))\n", "print(f\"first recorded step equals the hand-computed direction: \"\n", " f\"gradient descent {np.allclose(dx_gd, gd_info['dx'][0])}, \"\n", " f\"Newton {np.allclose(dx_newton, newton_info['dx'][0])}\")\n", "print(f\"|dx_GD| = {np.linalg.norm(dx_gd):.1f}, |dx_Newton| = {np.linalg.norm(dx_newton):.1f}, \"\n", " f\"angle between them = {np.degrees(np.arccos(cos_angle)):.0f} deg\")" ] }, { "cell_type": "markdown", "id": "2282cd82", "metadata": {}, "source": [ "Both recorded first steps are exactly $-\\nabla E$ and $-H^{-1}\\nabla E$, and already at rest they\n", "disagree: the Newton step is about 12 times shorter and points 62° away from $-\\nabla E$. Next,\n", "`iterates` rebuilds $x_0, x_1, \\dots$ from the recorded steps and `solver_metrics` measures each\n", "one. It forms $H$ at the gradient-descent iterates only to monitor $\\lambda$; gradient descent\n", "itself never forms $H$." ] }, { "cell_type": "code", "execution_count": 5, "id": "23e06f2c", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:26.799697Z", "iopub.status.busy": "2026-09-24T03:44:26.799621Z", "iopub.status.idle": "2026-09-24T03:44:26.842319Z", "shell.execute_reply": "2026-09-24T03:44:26.842024Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Newton : 6 iters, final |grad| = 2.26e-14, final E - E_Newton = 0.00e+00, final lambda = 2.46e-15\n", "Gradient descent : 60 iters, final |grad| = 6.09e-01, final E - E_Newton = 1.54e-01, final lambda = 5.08e-01\n" ] } ], "source": [ "def iterates(x0, info):\n", " \"\"\"x_0, x_1, ... rebuilt from the recorded steps x_{k+1} = x_k + alpha_k dx_k.\"\"\"\n", " xs = [x0]\n", " for alpha, dx in zip(info[\"alphas\"], info[\"dx\"]):\n", " xs.append(xs[-1] + alpha * dx)\n", " return xs\n", "\n", "def solver_metrics(xs):\n", " \"\"\"Energy, gradient norm and Newton decrement sqrt(g^T H^-1 g) at every iterate.\"\"\"\n", " energy, grad, decrement = [], [], []\n", " for x in xs:\n", " g = gradient_func(x)\n", " H_inv_g = sp.sparse.linalg.spsolve(hessian_func(x).tocsc(), g).reshape(-1, 1)\n", " energy.append(energy_func(x))\n", " grad.append(np.linalg.norm(g))\n", " decrement.append(np.sqrt(max((g.T @ H_inv_g).item(), 0.0)))\n", " return {\"energy\": energy, \"grad\": grad, \"decrement\": decrement}\n", "\n", "newton_xs = iterates(x0, newton_info)\n", "gd_xs = iterates(x0, gd_info)\n", "newton_metrics = solver_metrics(newton_xs)\n", "gd_metrics = solver_metrics(gd_xs)\n", "for name, xs, m in [(\"Newton\", newton_xs, newton_metrics), (\"Gradient descent\", gd_xs, gd_metrics)]:\n", " print(f\"{name:17s}: {len(xs) - 1:2d} iters, final |grad| = {m['grad'][-1]:.2e}, \"\n", " f\"final E - E_Newton = {m['energy'][-1] - newton_metrics['energy'][-1]:.2e}, \"\n", " f\"final lambda = {m['decrement'][-1]:.2e}\")" ] }, { "cell_type": "markdown", "id": "539b40bc", "metadata": {}, "source": [ "Newton reaches a round-off-level gradient in 6 iterations, while gradient descent uses all 60 and\n", "still sits 0.15 above Newton's energy." ] }, { "cell_type": "markdown", "id": "7791aaa4", "metadata": {}, "source": [ "## Checking the derivatives\n", "\n", "Both solvers trust `gradient_func`, and Newton also trusts `hessian_func`, so we check them against\n", "central differences (`simkit.gradient_cfd`): the gradient at a randomly perturbed rest state, and\n", "the Hessian there and at Newton's equilibrium $x^\\star$. `psd=True` projects each element Hessian to\n", "be positive semi-definite, so that $-H^{-1}\\nabla E$ is always a descent direction. The Hessian can\n", "therefore match only where no projection is active." ] }, { "cell_type": "code", "execution_count": 6, "id": "473d8234", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:26.844525Z", "iopub.status.busy": "2026-09-24T03:44:26.844180Z", "iopub.status.idle": "2026-09-24T03:44:26.867116Z", "shell.execute_reply": "2026-09-24T03:44:26.866717Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "gradient at perturbed rest: rel. error 2.6e-09\n", "Hessian at perturbed rest: rel. error 4.1e-02\n", "Hessian at equilibrium x*: rel. error 2.9e-11\n" ] } ], "source": [ "rng = np.random.default_rng(SEED)\n", "x_pert = x0 + FD_NOISE * rng.standard_normal(x0.shape)\n", "x_star = newton_xs[-1]\n", "\n", "g = gradient_func(x_pert)\n", "g_fd = simkit.gradient_cfd(lambda y: np.array([energy_func(y.reshape(-1, 1))]), x_pert.ravel(), FD_STEP)\n", "g_err = np.linalg.norm(g_fd.ravel() - g.ravel()) / np.linalg.norm(g)\n", "print(f\"gradient at perturbed rest: rel. error {g_err:.1e}\")\n", "for name, x in [(\"perturbed rest\", x_pert), (\"equilibrium x*\", x_star)]:\n", " H = hessian_func(x).toarray()\n", " H_fd = simkit.gradient_cfd(lambda y: gradient_func(y.reshape(-1, 1)).ravel(), x.ravel(), FD_STEP)\n", " H_err = np.linalg.norm(H_fd - H) / np.linalg.norm(H)\n", " print(f\"Hessian at {name}: rel. error {H_err:.1e}\")" ] }, { "cell_type": "markdown", "id": "52c98e91", "metadata": {}, "source": [ "The gradient matches to $10^{-9}$, and the Hessian matches at $x^\\star$ but differs by 4% at the\n", "perturbed state, where the projection is active." ] }, { "cell_type": "markdown", "id": "b5203eee", "metadata": {}, "source": [ "## Convergence curves\n", "\n", "Energy gap to the optimum, gradient norm and Newton decrement per iteration, all on a log scale." ] }, { "cell_type": "code", "execution_count": 7, "id": "50956b61", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:26.868152Z", "iopub.status.busy": "2026-09-24T03:44:26.868090Z", "iopub.status.idle": "2026-09-24T03:44:27.216061Z", "shell.execute_reply": "2026-09-24T03:44:27.215553Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, _ = utils.convergence_plot({\"Newton\": newton_metrics, \"Gradient Descent\": gd_metrics},\n", " title=\"Newton vs. Gradient Descent on the same problem\")\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"convergence.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"005_convergence.png\"))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "50156013", "metadata": {}, "source": [ "Newton's curves drop steeply, with the number of correct digits roughly doubling per step at the\n", "end (quadratic convergence). Gradient descent flattens out after about 10 iterations, stalled by the\n", "ill-conditioned elastic Hessian. Its $\\lambda$ stays near 0.5, and since $\\lambda^2/2$ estimates\n", "$E - E^\\star$, that predicts a remaining gap of about 0.13, close to the true 0.15. The accepted\n", "line-search step $\\alpha_k$, plotted next, shows why gradient descent stalls." ] }, { "cell_type": "code", "execution_count": 8, "id": "5a7cc3b0", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:27.217257Z", "iopub.status.busy": "2026-09-24T03:44:27.217171Z", "iopub.status.idle": "2026-09-24T03:44:27.318531Z", "shell.execute_reply": "2026-09-24T03:44:27.318159Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(6.5, 4))\n", "for name, info in [(\"Newton\", newton_info), (\"Gradient Descent\", gd_info)]:\n", " ax.semilogy(info[\"alphas\"], \"-o\", ms=3, color=utils.SOLVER_COLORS[name], label=name)\n", "ax.set_xlabel(\"iteration\")\n", "ax.set_ylabel(r\"accepted step $\\alpha_k$\")\n", "ax.set_title(\"line-search step size\")\n", "ax.grid(True, which=\"both\", color=\"0.9\", linewidth=0.7)\n", "ax.legend(fontsize=9)\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"step_sizes.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"005_step_sizes.png\"))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "eaa07fc6", "metadata": {}, "source": [ "Newton takes the full step $\\alpha = 1$ every time, while along $-\\nabla E$ the stiff directions\n", "dominate, so only a tiny step lowers the energy ($\\alpha = 1/16$ for the first two steps, then\n", "mostly $1/64$ with an occasional $1/32$)." ] }, { "cell_type": "markdown", "id": "c936e02a", "metadata": {}, "source": [ "## Watching the beam converge (one frame per iteration)\n", "\n", "Newton first: after one step the whole beam is already bent into nearly its final shape." ] }, { "cell_type": "code", "execution_count": 9, "id": "013f5f75", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:27.320033Z", "iopub.status.busy": "2026-09-24T03:44:27.319945Z", "iopub.status.idle": "2026-09-24T03:44:27.474551Z", "shell.execute_reply": "2026-09-24T03:44:27.474004Z" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fig, anim = utils.animate_mesh([x.reshape(n, dim) for x in newton_xs], T, lims=LIMS,\n", " title=\"Newton's method\", pin_pts=X[pin_idx],\n", " handle_traj=[x.reshape(n, dim)[handle_idx] for x in newton_xs],\n", " target_pts=[handle_targets] * len(newton_xs), fps=FPS_NEWTON)\n", "video = simkit.filesystem.save_animation(anim, os.path.join(RESULTS_DIR, \"newton.mp4\"), fps=FPS_NEWTON,\n", " copy_to=os.path.join(MEDIA_DIR, \"005_newton.mp4\"))\n", "plt.close(fig)\n", "utils.embed_video(video)" ] }, { "cell_type": "markdown", "id": "7d0e4b0f", "metadata": {}, "source": [ "Gradient descent: the handle reaches its target quickly, but the deformation only creeps back from\n", "the handle, leaving the left part of the beam nearly straight after 60 iterations." ] }, { "cell_type": "code", "execution_count": 10, "id": "3aa4090f", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:27.475705Z", "iopub.status.busy": "2026-09-24T03:44:27.475617Z", "iopub.status.idle": "2026-09-24T03:44:28.555525Z", "shell.execute_reply": "2026-09-24T03:44:28.555007Z" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fig, anim = utils.animate_mesh([x.reshape(n, dim) for x in gd_xs], T, lims=LIMS,\n", " title=\"Gradient descent\", pin_pts=X[pin_idx],\n", " handle_traj=[x.reshape(n, dim)[handle_idx] for x in gd_xs],\n", " target_pts=[handle_targets] * len(gd_xs), fps=FPS_GD)\n", "video = simkit.filesystem.save_animation(anim, os.path.join(RESULTS_DIR, \"gradient_descent.mp4\"),\n", " fps=FPS_GD,\n", " copy_to=os.path.join(MEDIA_DIR, \"005_gradient_descent.mp4\"))\n", "plt.close(fig)\n", "utils.embed_video(video)" ] }, { "cell_type": "markdown", "id": "cbb69a78", "metadata": {}, "source": [ "## Where the energy sits\n", "\n", "The per-element energy density $\\psi(F)$ at both final states, with $F$ from the same $J$ and the\n", "same $\\mu, \\lambda$ the energy uses, on one log color scale, and each vertex's distance between the\n", "gradient-descent result and $x^\\star$." ] }, { "cell_type": "code", "execution_count": 11, "id": "81e991ca", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:28.556839Z", "iopub.status.busy": "2026-09-24T03:44:28.556748Z", "iopub.status.idle": "2026-09-24T03:44:28.873615Z", "shell.execute_reply": "2026-09-24T03:44:28.873092Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "max psi: Newton 0.040, gradient descent 2.952; max vertex error of gradient descent 0.715\n" ] } ], "source": [ "F_newton = (J @ x_star).reshape(-1, dim, dim) # per-element F, as in the energy\n", "F_gd = (J @ gd_xs[-1]).reshape(-1, dim, dim)\n", "psi_newton = simkit.energies.elastic_energy_element_F(F_newton, mu, lam, MATERIAL).ravel()\n", "psi_gd = simkit.energies.elastic_energy_element_F(F_gd, mu, lam, MATERIAL).ravel()\n", "gd_error = np.linalg.norm((gd_xs[-1] - x_star).reshape(n, dim), axis=1)\n", "\n", "lims = utils.auto_limits([x_star.reshape(n, dim), gd_xs[-1].reshape(n, dim)], pad=0.1)\n", "fig, axes = plt.subplots(3, 1, figsize=(7.5, 8.5))\n", "utils.plot_scalar_field(axes[0], x_star.reshape(n, dim), T, psi_newton, lims=lims, cmap=\"magma\",\n", " norm=LogNorm(*PSI_RANGE), title=r\"Newton: energy density $\\psi$\", label=r\"$\\psi$\")\n", "utils.plot_scalar_field(axes[1], gd_xs[-1].reshape(n, dim), T, psi_gd, lims=lims, cmap=\"magma\",\n", " norm=LogNorm(*PSI_RANGE), title=r\"gradient descent: energy density $\\psi$\",\n", " label=r\"$\\psi$\")\n", "utils.plot_scalar_field(axes[2], gd_xs[-1].reshape(n, dim), T, gd_error, lims=lims,\n", " title=r\"gradient descent: distance to Newton's solution\",\n", " label=r\"$\\|x_i - x_i^\\star\\|$\")\n", "fig.tight_layout()\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"energy_density.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"005_energy_density.png\"))\n", "plt.show()\n", "print(f\"max psi: Newton {psi_newton.max():.3f}, gradient descent {psi_gd.max():.3f}; \"\n", " f\"max vertex error of gradient descent {gd_error.max():.3f}\")" ] }, { "cell_type": "markdown", "id": "6dec6ce6", "metadata": {}, "source": [ "Newton spreads a gentle bend along the whole beam (peak $\\psi = 0.04$), while gradient descent\n", "packs the strain into a kink by the handle (peak $\\psi = 2.95$), leaves the pinned half unstrained,\n", "and is off by up to 0.72 just before the kink." ] }, { "cell_type": "markdown", "id": "3d523b71", "metadata": {}, "source": [ "### Takeaways\n", "* **Newton** uses curvature and converges *quadratically*, which is ideal for stiff elasticity.\n", "* **Gradient descent** ignores curvature, gets tiny line-search steps, and stalls.\n", "* The **Newton decrement** is a clean, scale-aware stopping measure.\n", "* The Newton *step length* still needs care, which is the subject of tutorial 6." ] } ], "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": "3.12.13" } }, "nbformat": 4, "nbformat_minor": 5 }