{ "cells": [ { "cell_type": "markdown", "id": "0bc0bb61", "metadata": {}, "source": [ "# 6 · Why Line Search Matters\n", "\n", "A Newton *direction* $-H^{-1}\\nabla E$ points the right way, but the *step length* still matters: too\n", "large a step overshoots, inverts elements, and the energy **explodes** instead of decreasing.\n", "**Backtracking line search** starts from the full Newton step and shrinks it until the energy decreases\n", "enough (the Armijo condition). We drag a stiff beam's right edge slowly out and back, taking a few Newton\n", "iterations per frame, once with a fixed, too-large step and once with line search." ] }, { "cell_type": "markdown", "id": "dbd0c63e", "metadata": {}, "source": [ "Imports, and every tunable parameter of this notebook." ] }, { "cell_type": "code", "execution_count": 1, "id": "e679836e", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:26.040058Z", "iopub.status.busy": "2026-09-24T03:44:26.039842Z", "iopub.status.idle": "2026-09-24T03:44:26.610892Z", "shell.execute_reply": "2026-09-24T03:44:26.610254Z" } }, "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 TwoSlopeNorm\n", "import igl\n", "import simkit\n", "import utils\n", "\n", "NOTEBOOK = \"006_line_search\" # this file's name\n", "RESULTS_DIR = utils.notebook_results_path(NOTEBOOK) # results/006_line_search/\n", "MEDIA_DIR = \"media\" # tracked copies for the website\n", "# mesh: a thick beam\n", "NX, NY = 16, 7 # grid vertices along x and y\n", "WIDTH, HEIGHT = 2.0, 0.6 # beam size\n", "# material: stiff and nearly incompressible\n", "YM = 50.0 # Young's modulus\n", "PR = 0.49 # Poisson ratio (nearly incompressible)\n", "MATERIAL = \"macklin-mueller-neo-hookean\" # Neo-Hookean elastic energy\n", "K_PIN = 1e6 # penalty stiffness of the pin and of the handle\n", "# handle motion\n", "HANDLE_TRAVEL = 1.0 # how far the handle slides to the right\n", "N_RAMP = 22 # frames out (and as many back)\n", "# Newton\n", "ITERS_PER_FRAME = 2 # Newton iterations per handle position\n", "FIXED_STEP = 2.0 # the deliberately too-large fixed step t (in Newton steps)\n", "ARMIJO_C = 0.01 # Armijo sufficient-decrease constant c\n", "BACKTRACK_BETA = 0.5 # step shrink factor per backtracking trial\n", "DIVERGE = 1e3 # max |x| above this counts as blown up\n", "# validation\n", "FD_STEP = 1e-5 # central-difference step of the gradient check\n", "FD_NOISE = 0.01 # random perturbation of the rest state for that check\n", "SEED = 0 # random seed of that perturbation\n", "T_MAX_PROFILE = 2.5 # largest step t sampled along one Newton direction\n", "N_PROFILE = 101 # number of samples along it\n", "# video\n", "FPS_FIXED = 12 # frame rate of the (short) exploding run\n", "FPS_LS = 20 # frame rate of the line-search run" ] }, { "cell_type": "markdown", "id": "21d67a22", "metadata": {}, "source": [ "## A thick, stiff beam and its handle path\n", "\n", "A thick $2 \\times 0.6$ grid from libigl: the left edge is pinned (blue squares) and the whole right edge\n", "is the handle (orange). The handle slides `HANDLE_TRAVEL` to the right over `N_RAMP` frames and then\n", "back; the figure shows the rest mesh and that path." ] }, { "cell_type": "code", "execution_count": 2, "id": "d81e40f3", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:26.612747Z", "iopub.status.busy": "2026-09-24T03:44:26.612595Z", "iopub.status.idle": "2026-09-24T03:44:26.731386Z", "shell.execute_reply": "2026-09-24T03:44:26.730762Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "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", "pin_idx = np.where(X[:, 0] <= X[:, 0].min() + 1e-6)[0] # left edge\n", "handle_idx = np.where(X[:, 0] >= X[:, 0].max() - 1e-6)[0] # right edge\n", "\n", "ramp = np.concatenate([np.linspace(0, 1, N_RAMP), np.linspace(1, 0, N_RAMP)]) # right, then back\n", "handle_offsets = ramp[:, None] * np.array([HANDLE_TRAVEL, 0.0]) # (frames, 2)\n", "\n", "(x_lo, x_hi), y_lims = utils.auto_limits([X], pad=0.15)\n", "fig, (ax_mesh, ax_ramp) = plt.subplots(1, 2, figsize=(12, 3.4), gridspec_kw={\"width_ratios\": [1.7, 1]})\n", "utils.plot_mesh(ax_mesh, X, T, pins=pin_idx, handles=handle_idx,\n", " title=f\"rest mesh: {n} vertices, {len(T)} triangles\",\n", " lims=((x_lo, x_hi + 0.2), y_lims)) # extra room on the right for the legend\n", "ax_ramp.plot(handle_offsets[:, 0], \"o-\", ms=3, color=utils.HANDLE_C)\n", "ax_ramp.set(xlabel=\"frame\", ylabel=\"handle x-offset\", title=\"handle path: out and back\")\n", "ax_ramp.grid(True, color=\"0.9\")\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, \"006_mesh.png\"))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "f14566fe", "metadata": {}, "source": [ "## The beam system\n", "\n", "`beam_system` returns the energy, gradient and Hessian of Neo-Hookean elasticity plus a soft spring for\n", "the pin and one for the handle, one term per line. The beam is thick (bending stores more energy) and\n", "nearly incompressible ($\\nu = 0.49$ resists volume change), so an over-eager step bites fast. The\n", "Armijo test compares the energy with the gradient's prediction, so the cell ends by checking\n", "`gradient_func` against central differences (`simkit.gradient_cfd`); the relative error should be tiny." ] }, { "cell_type": "code", "execution_count": 3, "id": "9682b477", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:26.732787Z", "iopub.status.busy": "2026-09-24T03:44:26.732711Z", "iopub.status.idle": "2026-09-24T03:44:26.755912Z", "shell.execute_reply": "2026-09-24T03:44:26.755473Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "gradient check: relative error 2.5e-10\n" ] } ], "source": [ "J = simkit.deformation_jacobian(X, T)\n", "vol = simkit.volume(X, T)\n", "mu, lam = simkit.ympr_to_lame(YM, PR)\n", "mu = np.full((len(T), 1), mu)\n", "lam = np.full((len(T), 1), lam)\n", "Q_pin, b_pin = simkit.dirichlet_penalty(pin_idx, X[pin_idx], n, K_PIN) # the pin never moves\n", "\n", "def beam_system(handle_targets):\n", " \"\"\"Neo-Hookean beam + soft pin (left edge) + soft handle (right edge) pulled to handle_targets.\"\"\"\n", " Q_handle, b_handle = simkit.dirichlet_penalty(handle_idx, handle_targets, n, K_PIN)\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\n", "\n", "# gradient check at a randomly perturbed rest state, with the handle at its farthest target\n", "energy_func, gradient_func, _ = beam_system(X[handle_idx] + handle_offsets[N_RAMP - 1])\n", "x_test = X.reshape(-1) + FD_NOISE * np.random.default_rng(SEED).standard_normal(n * dim)\n", "g_fd = simkit.gradient_cfd(lambda y: np.array(energy_func(y.reshape(-1, 1))), x_test, FD_STEP)\n", "g_an = gradient_func(x_test.reshape(-1, 1)).ravel()\n", "print(f\"gradient check: relative error {np.linalg.norm(g_an - g_fd) / np.linalg.norm(g_an):.1e}\")" ] }, { "cell_type": "markdown", "id": "5b90cf6e", "metadata": {}, "source": [ "## The quasi-static driver\n", "\n", "At each handle position we take `ITERS_PER_FRAME` Newton iterations: solve $H\\,\\Delta x = -g$, then step\n", "$x \\leftarrow x + t\\,\\Delta x$. The two runs differ only in $t$: a fixed `FIXED_STEP` $= 2$, or the step\n", "chosen by `simkit.backtracking_line_search`, which tries $t = 1$ and multiplies it by `BACKTRACK_BETA`\n", "until the Armijo condition holds (with line search this is one iteration of\n", "`simkit.solvers.newton_solver`). The printout says when the fixed-step run blows up and how often the\n", "line search kept the full Newton step.\n", "\n", "$$E(x + t\\,\\Delta x) \\;\\le\\; E(x) + c\\,t\\,g^\\top \\Delta x$$" ] }, { "cell_type": "code", "execution_count": 4, "id": "4e29a011", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:26.757251Z", "iopub.status.busy": "2026-09-24T03:44:26.757145Z", "iopub.status.idle": "2026-09-24T03:44:26.913078Z", "shell.execute_reply": "2026-09-24T03:44:26.912668Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "fixed step t = 2 (no line search): blew up at frame 9 of 44\n", "line search: completed 44 of 44 frames; kept the full step t = 1 in 88 of 88 iterations\n" ] } ], "source": [ "def drive(use_line_search):\n", " \"\"\"Sweep the handle along handle_offsets; return each frame's final state, every step t taken,\n", " and the frame where the run blew up (None if it never did).\"\"\"\n", " x = X.reshape(-1, 1).copy()\n", " states, steps = [], []\n", " blew_at = None\n", " for offset in handle_offsets:\n", " energy_func, gradient_func, hessian_func = beam_system(X[handle_idx] + offset)\n", " for _ in range(ITERS_PER_FRAME):\n", " g = gradient_func(x)\n", " H = hessian_func(x)\n", " dx = sp.sparse.linalg.spsolve(H.tocsc(), -g).reshape(-1, 1) # Newton direction\n", " if use_line_search:\n", " t = simkit.backtracking_line_search(energy_func, x, g, dx,\n", " alpha=ARMIJO_C, beta=BACKTRACK_BETA)[0]\n", " else:\n", " t = FIXED_STEP\n", " x = x + t * dx\n", " steps.append(t)\n", " states.append(x.reshape(n, dim).copy())\n", " if not np.all(np.isfinite(x)) or np.abs(x).max() > DIVERGE:\n", " blew_at = len(states) - 1\n", " break\n", " return states, np.array(steps), blew_at\n", "\n", "fixed_states, fixed_steps, blew_at = drive(use_line_search=False)\n", "ls_states, ls_steps, _ = drive(use_line_search=True)\n", "if blew_at is None:\n", " print(f\"fixed step t = {FIXED_STEP:g} (no line search): survived all {len(fixed_states)} frames\")\n", "else:\n", " print(f\"fixed step t = {FIXED_STEP:g} (no line search): blew up at frame {blew_at} of {len(handle_offsets)}\")\n", "print(f\"line search: completed {len(ls_states)} of {len(handle_offsets)} frames; kept the full step t = 1 in \"\n", " f\"{np.sum(ls_steps == 1.0)} of {len(ls_steps)} iterations\")" ] }, { "cell_type": "markdown", "id": "04bc1fd3", "metadata": {}, "source": [ "## Without line search: the solver explodes\n", "\n", "With $t = 2$ each step lands as far past the minimum as it started before it, so the error is mirrored,\n", "never removed. Watch the orange handle vertices: they never leave $x = 1$ while their targets (grey\n", "crosses) slide right, because each frame's two mirrored steps cancel, so they fall further behind every\n", "frame and the wobble this drives grows until elements invert (frame 8) and the next step flings the mesh\n", "off screen (frame 9)." ] }, { "cell_type": "code", "execution_count": 5, "id": "e04d0e05", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:26.914327Z", "iopub.status.busy": "2026-09-24T03:44:26.914256Z", "iopub.status.idle": "2026-09-24T03:44:27.129991Z", "shell.execute_reply": "2026-09-24T03:44:27.129548Z" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lims = utils.auto_limits(ls_states + fixed_states[:blew_at], pad=0.3) # every frame but the blow-up\n", "fig, anim = utils.animate_mesh(fixed_states, T, lims=lims,\n", " title=\"Fixed step, NO line search -> explodes\", pin_pts=X[pin_idx],\n", " handle_traj=[s[handle_idx] for s in fixed_states],\n", " target_pts=[X[handle_idx] + offset for offset in handle_offsets[:len(fixed_states)]],\n", " fps=FPS_FIXED)\n", "video = simkit.filesystem.save_animation(anim, os.path.join(RESULTS_DIR, \"no_line_search.mp4\"), fps=FPS_FIXED,\n", " copy_to=os.path.join(MEDIA_DIR, \"006_no_line_search.mp4\"))\n", "plt.close(fig)\n", "utils.embed_video(video)" ] }, { "cell_type": "markdown", "id": "261c027b", "metadata": {}, "source": [ "## With line search: smooth and stable\n", "\n", "The same sweep with backtracking line search follows the handle out and back without a hitch." ] }, { "cell_type": "code", "execution_count": 6, "id": "2cb0e164", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:27.131261Z", "iopub.status.busy": "2026-09-24T03:44:27.131163Z", "iopub.status.idle": "2026-09-24T03:44:27.895713Z", "shell.execute_reply": "2026-09-24T03:44:27.895255Z" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fig, anim = utils.animate_mesh(ls_states, T, lims=lims,\n", " title=\"Backtracking line search -> stable\", pin_pts=X[pin_idx],\n", " handle_traj=[s[handle_idx] for s in ls_states], fps=FPS_LS)\n", "video = simkit.filesystem.save_animation(anim, os.path.join(RESULTS_DIR, \"line_search.mp4\"), fps=FPS_LS,\n", " copy_to=os.path.join(MEDIA_DIR, \"006_line_search.mp4\"))\n", "plt.close(fig)\n", "utils.embed_video(video)" ] }, { "cell_type": "markdown", "id": "eeaaa35d", "metadata": {}, "source": [ "## Why it fails: per-frame diagnostics\n", "\n", "For each frame's final state we plot the gradient norm $\\|\\nabla E\\|$ (distance from equilibrium) and\n", "the smallest $\\det F$ over all triangles (below zero means inverted; values below the panel are marked\n", "on its lower edge). The printout compares the two runs' energies at the blow-up frame: the fixed-step\n", "energy has exploded to about $10^{19}$, while the line-search value is negative only because the soft\n", "springs drop their constant $\\tfrac12 K\\|y\\|^2$ (only differences matter)." ] }, { "cell_type": "code", "execution_count": 7, "id": "8638f997", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:27.897499Z", "iopub.status.busy": "2026-09-24T03:44:27.897388Z", "iopub.status.idle": "2026-09-24T03:44:28.147873Z", "shell.execute_reply": "2026-09-24T03:44:28.147447Z" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "blow-up frame 9: energy 1.07e+19 (fixed step) vs -1.09e+07 (line search)\n" ] } ], "source": [ "def frame_diagnostics(states):\n", " \"\"\"Energy, gradient norm and smallest det F of each frame's final state.\"\"\"\n", " E, g_norm, det_min = [], [], []\n", " for state, offset in zip(states, handle_offsets):\n", " energy_func, gradient_func, _ = beam_system(X[handle_idx] + offset)\n", " x = state.reshape(-1, 1)\n", " E.append(energy_func(x))\n", " g_norm.append(np.linalg.norm(gradient_func(x)))\n", " det_min.append(np.linalg.det(simkit.deformation_gradient(X, T, state)).min())\n", " return np.array(E), np.array(g_norm), np.array(det_min)\n", "\n", "E_fixed, g_fixed, det_fixed = frame_diagnostics(fixed_states)\n", "E_ls, g_ls, det_ls = frame_diagnostics(ls_states)\n", "runs = {\"fixed step\": (g_fixed, det_fixed, \"#d62728\"), \"line search\": (g_ls, det_ls, \"#1f77b4\")}\n", "\n", "fig, (ax_g, ax_d) = plt.subplots(1, 2, figsize=(11, 3.8))\n", "for name, (g_norm, det_min, color) in runs.items():\n", " ax_g.semilogy(g_norm, \"o-\", ms=3, color=color, label=name)\n", " ax_d.plot(det_min, \"o-\", ms=3, color=color, label=name)\n", "ax_g.set(xlabel=\"frame\", ylabel=r\"$\\|\\nabla E\\|$\", title=\"gradient norm after each frame\")\n", "det_floor = -1.5 # lower edge of the det F panel\n", "off_scale = np.flatnonzero(det_fixed < det_floor) # fixed-step frames below that edge\n", "ax_d.plot(off_scale, np.full(len(off_scale), det_floor + 0.08), \"v\", color=\"#d62728\", ms=9,\n", " label=\"fixed step, off scale\")\n", "if len(off_scale):\n", " ax_d.annotate(\"\\n\".join(f\"frame {k}: {det_fixed[k]:.2g}\" for k in off_scale),\n", " (off_scale[-1], det_floor + 0.08), xytext=(10, 0), textcoords=\"offset points\",\n", " va=\"bottom\", color=\"#d62728\", fontsize=9)\n", "ax_d.axhline(0.0, color=\"0.3\", lw=1, ls=\"--\")\n", "ax_d.set(xlabel=\"frame\", ylabel=r\"min $\\det F$\", title=r\"smallest $\\det F$ (< 0: inverted)\",\n", " ylim=(det_floor, 1.2))\n", "for ax in (ax_g, ax_d):\n", " ax.grid(True, color=\"0.9\")\n", " ax.legend(fontsize=9)\n", "fig.tight_layout()\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"diagnostics.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"006_diagnostics.png\"))\n", "plt.show()\n", "k_end = len(fixed_states) - 1 # the blow-up frame, if there was one\n", "frame_name = \"blow-up frame\" if blew_at is not None else \"last frame (no blow-up)\"\n", "print(f\"{frame_name} {k_end}: energy {E_fixed[k_end]:.2e} (fixed step) vs {E_ls[k_end]:.2e} (line search)\")" ] }, { "cell_type": "markdown", "id": "a405db8f", "metadata": {}, "source": [ "The fixed step's gradient norm sits more than eight orders of magnitude above the line-search run and\n", "grows with every frame, and its smallest $\\det F$ drops below zero at frame 8, one frame before the\n", "blow-up. The line-search run stays near equilibrium with $\\det F \\ge 0.9$ throughout." ] }, { "cell_type": "markdown", "id": "2148071b", "metadata": {}, "source": [ "## Inverted elements, triangle by triangle\n", "\n", "$\\det F$ per triangle at the first frame where the fixed-step run has inverted elements, next to the\n", "line-search run at the same frame (red: inverted, $\\det F < 0$; blue: not inverted)." ] }, { "cell_type": "code", "execution_count": 8, "id": "58bc58be", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:28.149389Z", "iopub.status.busy": "2026-09-24T03:44:28.149266Z", "iopub.status.idle": "2026-09-24T03:44:28.319384Z", "shell.execute_reply": "2026-09-24T03:44:28.318971Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "inverted_frames = np.flatnonzero(det_fixed < 0)\n", "assert len(inverted_frames) and inverted_frames[0] >= 1, \"the fixed-step run never inverted; raise FIXED_STEP\"\n", "k_bad = int(inverted_frames[0]) # first frame with inverted triangles\n", "fig, axes = plt.subplots(1, 2, figsize=(12, 3.8))\n", "field_lims = utils.auto_limits([fixed_states[k_bad], ls_states[k_bad]], pad=0.1)\n", "for ax, (name, states) in zip(axes, [(\"fixed step\", fixed_states), (\"line search\", ls_states)]):\n", " det_F = np.linalg.det(simkit.deformation_gradient(X, T, states[k_bad]))\n", " utils.plot_scalar_field(ax, states[k_bad], T, det_F, cmap=\"RdBu\", norm=TwoSlopeNorm(vcenter=0.0, vmin=-2.0, vmax=2.0),\n", " lims=field_lims, label=r\"$\\det F$\",\n", " title=f\"{name}, frame {k_bad}: {np.sum(det_F < 0)} inverted\")\n", "fig.tight_layout()\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"det_F.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"006_det_F.png\"))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "191c06d9", "metadata": {}, "source": [ "## The energy along one Newton direction\n", "\n", "At the start of that frame (the fixed-step run's last state without inverted triangles) we sample\n", "$E(x + t\\,\\Delta x) - E(x)$ along the Newton direction. It is a near-parabola with its minimum at $t = 1$.\n", "Steps in the green band pass the Armijo test (curve below the dashed line); $t = 2$ lands back at the\n", "starting energy, outside it, and the right panel shows it squeezing triangles almost flat. The star is\n", "where backtracking would end if it started from $t = 2$." ] }, { "cell_type": "code", "execution_count": 9, "id": "34ca3b3d", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:28.320467Z", "iopub.status.busy": "2026-09-24T03:44:28.320384Z", "iopub.status.idle": "2026-09-24T03:44:28.473759Z", "shell.execute_reply": "2026-09-24T03:44:28.473035Z" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "E(x + 2 dx) - E(x) = 51.9 (Armijo needs <= -2.03e+04); backtracking accepts t = 1\n" ] } ], "source": [ "x0 = fixed_states[k_bad - 1].reshape(-1, 1)\n", "energy_func, gradient_func, hessian_func = beam_system(X[handle_idx] + handle_offsets[k_bad])\n", "g = gradient_func(x0)\n", "dx = sp.sparse.linalg.spsolve(hessian_func(x0).tocsc(), -g).reshape(-1, 1)\n", "ts = np.linspace(0.0, T_MAX_PROFILE, N_PROFILE)\n", "dE = np.array([energy_func(x0 + t * dx) for t in ts]) - energy_func(x0)\n", "armijo = ARMIJO_C * ts * (g.T @ dx).item()\n", "det_min_t = np.array([np.linalg.det(simkit.deformation_gradient(X, T, (x0 + t * dx).reshape(n, dim))).min()\n", " for t in ts])\n", "t_back = FIXED_STEP * simkit.backtracking_line_search(energy_func, x0, g, FIXED_STEP * dx,\n", " alpha=ARMIJO_C, beta=BACKTRACK_BETA)[0]\n", "\n", "fig, (ax_e, ax_d) = plt.subplots(1, 2, figsize=(11, 3.8))\n", "ax_e.plot(ts, dE, color=\"k\", lw=2, label=r\"$E(x+t\\Delta x)-E(x)$\")\n", "ax_e.plot(ts, armijo, \"--\", color=\"0.4\", label=r\"Armijo line $c\\,t\\,g^\\top\\Delta x$\")\n", "ax_e.fill_between(ts, dE.min() * 1.1, dE.max(), where=dE <= armijo, color=\"#2ca02c\", alpha=0.15,\n", " label=\"Armijo accepts\")\n", "for ax, ys in ((ax_e, dE), (ax_d, det_min_t)):\n", " ax.plot([1.0], [np.interp(1.0, ts, ys)], \"o\", color=\"#1f77b4\", ms=9, label=\"Newton step t = 1\")\n", " ax.plot([FIXED_STEP], [np.interp(FIXED_STEP, ts, ys)], \"X\", color=\"#d62728\", ms=10,\n", " label=f\"fixed step t = {FIXED_STEP:g}\")\n", " ax.plot([t_back], [np.interp(t_back, ts, ys)], \"*\", color=\"#2ca02c\", ms=14, mfc=\"none\", mew=1.5,\n", " label=f\"backtracked from t = {FIXED_STEP:g}\")\n", " ax.set_xlabel(\"step length t\")\n", " ax.grid(True, color=\"0.9\")\n", "ax_e.set(title=f\"energy along the Newton direction (frame {k_bad})\", ylabel=\"energy change\")\n", "ax_d.axhline(0.0, color=\"0.3\", lw=1, ls=\"--\")\n", "ax_d.plot(ts, det_min_t, color=\"k\", lw=2)\n", "ax_d.set(title=r\"smallest $\\det F$ along the same direction\", ylabel=r\"min $\\det F$\")\n", "ax_e.legend(fontsize=8, loc=\"upper left\")\n", "fig.tight_layout()\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"energy_along_step.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"006_energy_along_step.png\"))\n", "plt.show()\n", "print(f\"E(x + {FIXED_STEP:g} dx) - E(x) = {np.interp(FIXED_STEP, ts, dE):.3g} \"\n", " f\"(Armijo needs <= {np.interp(FIXED_STEP, ts, armijo):.3g}); backtracking accepts t = {t_back:g}\")" ] }, { "cell_type": "markdown", "id": "2c6e91b9", "metadata": {}, "source": [ "### Takeaways\n", "* A good Newton *direction* isn't enough: an unchecked **step length** can diverge (here $t = 2$ mirrors\n", " the error instead of removing it, until triangles invert).\n", "* **Backtracking line search** shrinks the step until the energy decreases enough (Armijo).\n", "* Cheap insurance: here it kept the full Newton step every time, so it cost two energy evaluations per\n", " iteration and bought a solver that won't blow up." ] } ], "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 }