{ "cells": [ { "cell_type": "markdown", "id": "118cf98d", "metadata": {}, "source": [ "# Shape optimization with a level-set parameterization (JAX version)\n", "In this example we use the `LevelSetParameterization` class to perform a free-form shape optimization in which the demag field is the only actuator. A soft-magnetic 2D element starts as a rectangle elongated along $x$ with uniform magnetization $\\vec{m} = \\vec{e}_x$ -- its shape-anisotropy easy axis, i.e. an equilibrium. The RBF amplitudes of the level-set parameterization (the element's shape) are optimized such that the magnetization, relaxing for $T = 2\\,\\text{ns}$ under exchange and demag interaction only, ends up along $+y$:\n", "\n", "$$\n", "\\mathcal{L}(\\vec{s}) = \\frac{\\int_\\Omega \\rho(\\vec{s}) \\, \\|\\vec{m}(T) - \\vec{m}_\\text{target}\\|^2 \\,\\text{d}V}{\\int_\\Omega \\rho(\\vec{s}) \\,\\text{d}V},\n", "\\qquad \\vec{m}_\\text{target} = \\vec{e}_y.\n", "$$\n", "\n", "Since the easy axis follows the shape, the optimizer has to rotate the element's elongation from $x$ to $y$. The level-set parameterization is free to change the topology of the design along the way -- nucleating holes or splitting the element into several islands -- which distinguishes it from boundary-based shape optimization." ] }, { "cell_type": "markdown", "id": "a5309065", "metadata": {}, "source": [ "### Import libraries\n", "Import libraries and set the backend to JAX. The level-set smooth maximum requires `float64`: under `float32` it loses accuracy, and reverse-mode gradients through the LLG time integration have been observed to be NaN while the forward pass looks healthy. The dtype must be set before any tensor is created." ] }, { "cell_type": "code", "execution_count": 1, "id": "3e62962d", "metadata": { "execution": { "iopub.execute_input": "2026-09-03T13:09:13.436074Z", "iopub.status.busy": "2026-09-03T13:09:13.435910Z", "iopub.status.idle": "2026-09-03T13:09:19.426410Z", "shell.execute_reply": "2026-09-03T13:09:19.425583Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/av09084/envs/neuralmag_nodefix/lib/python3.13/site-packages/tqdm/auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html\n", " from .autonotebook import tqdm as notebook_tqdm\n", "2026-09-03 15:09:18 NeuralMag:INFO \u001b[1;37;32m[NeuralMag] Version 1.0.0\u001b[0m\n", "2026-09-03 15:09:19 NeuralMag:INFO \u001b[1;37;32m[NeuralMag] Backend set to 'jax'.\u001b[0m\n", "2026-09-03 15:09:19 NeuralMag:INFO \u001b[1;37;32m[NeuralMag] Set default dtype to 'float64'.\u001b[0m\n" ] } ], "source": [ "import equinox as eqx\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import optax\n", "from tqdm import tqdm\n", "\n", "import neuralmag as nm\n", "\n", "nm.config.backend = \"jax\"\n", "nm.config.dtype = \"float64\"" ] }, { "cell_type": "markdown", "id": "b0b90da2", "metadata": {}, "source": [ "### Setup mesh and state\n", "Setup mesh, state and material parameters. The damping is set to $\\alpha = 1$: only the final state matters in this example, not the dynamics of $\\vec{m}$, so the strongly overdamped $\\vec{m}(T)$ approximates the equilibrium of the current shape rather than a mid-precession snapshot." ] }, { "cell_type": "code", "execution_count": 2, "id": "e9e99642", "metadata": { "execution": { "iopub.execute_input": "2026-09-03T13:09:19.428711Z", "iopub.status.busy": "2026-09-03T13:09:19.428431Z", "iopub.status.idle": "2026-09-03T13:09:20.673611Z", "shell.execute_reply": "2026-09-03T13:09:20.672646Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "2026-09-03 15:09:19 NeuralMag:INFO \u001b[1;37;32m[Mesh] 2D, 32 x 32 (size = 5e-09 x 5e-09 x 5e-09)\u001b[0m\n", "2026-09-03 15:09:20 NeuralMag:INFO \u001b[1;37;32m[NeuralMag] Set default device to 'cpu:0'.\u001b[0m\n", "2026-09-03 15:09:20 NeuralMag:INFO \u001b[1;37;32m[State] Running on device: cpu:0 (dtype = float64, backend = jax)\u001b[0m\n" ] } ], "source": [ "mesh = nm.Mesh((32, 32), (5e-9, 5e-9, 5e-9))\n", "state = nm.State(mesh)\n", "\n", "state.material.Ms = 8e5\n", "state.material.A = 1.3e-11\n", "state.material.alpha = 1.0" ] }, { "cell_type": "markdown", "id": "7ce03be5", "metadata": {}, "source": [ "### Set up the level-set parameterization\n", "The design region covers the mesh up to a 2-cell border. Note that outside the design region the parameterization places *material* ($\\rho = 1$), so that a design can be embedded in a fixed layout; here the `geometry` mask turns that border into permanent void instead, keeping the element away from the mesh edge.\n", "\n", "The initial shape is a rectangle elongated along $x$ (half-widths 12 x 6 cells): positive amplitudes inside, negative outside put the level-set interface at the rectangle's edge. The interface must lie inside the mesh -- if the sigmoid saturates everywhere (no interface), the gradient with respect to the amplitudes is exactly zero and the optimization cannot start.\n", "\n", "`sigmoid_a` sets the interface width: with the default Eikonal renormalization the 10--90 % transition of $\\rho$ spans about $4/a$ cells, so `sigmoid_a=3` gives an interface about 1.3 cells wide, independently of the design and of the filter width." ] }, { "cell_type": "code", "execution_count": 3, "id": "9913afea", "metadata": { "execution": { "iopub.execute_input": "2026-09-03T13:09:20.675366Z", "iopub.status.busy": "2026-09-03T13:09:20.675210Z", "iopub.status.idle": "2026-09-03T13:09:20.722059Z", "shell.execute_reply": "2026-09-03T13:09:20.721317Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "2026-09-03 15:09:20 NeuralMag:INFO \u001b[1;37;32m[LevelSetParameterization] Register state method 'rho' (10x10 RBFs on cells x(2, 30), y(2, 30))\u001b[0m\n" ] } ], "source": [ "NUM_RBFS = 10\n", "BORDER = 2\n", "\n", "geometry = np.ones(mesh.n)\n", "geometry[:BORDER, :] = geometry[-BORDER:, :] = 0.0\n", "geometry[:, :BORDER] = geometry[:, -BORDER:] = 0.0\n", "\n", "lsf = nm.LevelSetParameterization(\n", " NUM_RBFS,\n", " NUM_RBFS,\n", " xlimits=(BORDER, mesh.n[0] - BORDER),\n", " ylimits=(BORDER, mesh.n[1] - BORDER),\n", " geometry=geometry,\n", " sigmoid_a=3.0,\n", ")\n", "lsf.register(state)\n", "\n", "centers_x = np.linspace(BORDER, mesh.n[0] - BORDER, NUM_RBFS)\n", "centers_y = np.linspace(BORDER, mesh.n[1] - BORDER, NUM_RBFS)\n", "cx, cy = np.meshgrid(centers_x, centers_y, indexing=\"ij\")\n", "inside = (np.abs(cx - mesh.n[0] / 2) < 12.0) & (np.abs(cy - mesh.n[1] / 2) < 6.0)\n", "state.rbf_amplitudes = state.tensor(np.where(inside, 2.0, -2.0))\n", "\n", "rho_func = state.resolve(\"rho\", [\"rbf_amplitudes\"])" ] }, { "cell_type": "markdown", "id": "8b4bf57e", "metadata": {}, "source": [ "### Set up magnetization and effective field\n", "The magnetization starts uniformly along $+x$, the easy axis of the initial rectangle. The torque on this initial configuration is close to zero -- but the gradient with respect to the amplitudes is not, since asymmetric shape changes tilt the demag field. The magnetization is defined as a cell function on the same grid as $\\rho$, so the loss needs no interpolation between nodes and cells. The effective field consists of exchange and demag interaction only -- there is no external field in this example." ] }, { "cell_type": "code", "execution_count": 4, "id": "0b823f57", "metadata": { "execution": { "iopub.execute_input": "2026-09-03T13:09:20.724521Z", "iopub.status.busy": "2026-09-03T13:09:20.724351Z", "iopub.status.idle": "2026-09-03T13:09:21.155928Z", "shell.execute_reply": "2026-09-03T13:09:21.155097Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "2026-09-03 15:09:20 NeuralMag:INFO \u001b[1;37;32m[ExchangeField] Register state methods (field: 'h_exchange', energy: 'E_exchange', energy density: 'e_exchange')\u001b[0m\n", "2026-09-03 15:09:20 NeuralMag:INFO \u001b[1;37;32m[DemagField] Register state methods (field: 'h_demag', energy: 'E_demag', energy density: 'e_demag')\u001b[0m\n", "2026-09-03 15:09:20 NeuralMag:INFO \u001b[1;37;32m[DemagField]: building the demag tensor on the CPU (NumPy). Set NM_JAX_GPU_SETUP=1 or pass gpu_setup=True (requires PyTorch and a CUDA GPU) to build it on the GPU -- much faster for large meshes.\u001b[0m\n", "2026-09-03 15:09:20 NeuralMag:INFO \u001b[1;37;32m[DemagField]: Set up demag tensor\u001b[0m\n", "2026-09-03 15:09:21 NeuralMag:INFO \u001b[1;37;32m[TotalField] Register state methods (field: 'h', energy: 'E', energy density: 'e')\u001b[0m\n" ] } ], "source": [ "state.m = nm.VectorCellFunction(state).fill((1.0, 0.0, 0.0))\n", "\n", "nm.ExchangeField().register(state, \"exchange\")\n", "nm.DemagField().register(state, \"demag\")\n", "nm.TotalField(\"exchange\", \"demag\").register(state)" ] }, { "cell_type": "markdown", "id": "1297dce3", "metadata": {}, "source": [ "### Set up LLGSolver\n", "The RBF amplitudes are registered as solver parameters in order to allow for efficient adjoint gradient computation through the time integration." ] }, { "cell_type": "code", "execution_count": 5, "id": "7a46d155", "metadata": { "execution": { "iopub.execute_input": "2026-09-03T13:09:21.158157Z", "iopub.status.busy": "2026-09-03T13:09:21.157998Z", "iopub.status.idle": "2026-09-03T13:09:21.170030Z", "shell.execute_reply": "2026-09-03T13:09:21.169329Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "2026-09-03 15:09:21 NeuralMag:INFO \u001b[1;37;32m[LLGSolverJAX] Initialize RHS function\u001b[0m\n" ] } ], "source": [ "llg = nm.LLGSolver(state, parameters=[\"rbf_amplitudes\"])\n", "\n", "ts = state.tensor([0.0, 2e-9])\n", "m_target = state.tensor([0.0, 1.0, 0.0])" ] }, { "cell_type": "markdown", "id": "fba345d9", "metadata": {}, "source": [ "### Define loss function\n", "The loss is the $\\rho$-weighted misalignment between $\\vec{m}(T)$ and the target direction. The weighting keeps the void region -- where the magnetization is physically meaningless -- out of the loss, and the normalization avoids rewarding plain material removal. The `filter_value_and_grad` decorator enriches the return value of the loss with its gradient." ] }, { "cell_type": "code", "execution_count": 6, "id": "ba0c5869", "metadata": { "execution": { "iopub.execute_input": "2026-09-03T13:09:21.171533Z", "iopub.status.busy": "2026-09-03T13:09:21.171373Z", "iopub.status.idle": "2026-09-03T13:09:21.174087Z", "shell.execute_reply": "2026-09-03T13:09:21.173471Z" } }, "outputs": [], "source": [ "@eqx.filter_value_and_grad\n", "def grad_loss(amps):\n", " m_T = llg.solve(ts, amps).ys[-1]\n", " rho = rho_func(amps)\n", " return (rho * ((m_T - m_target) ** 2).sum(-1)).sum() / rho.sum()" ] }, { "cell_type": "markdown", "id": "35cbbbb2", "metadata": {}, "source": [ "### Define plot function\n", "Visualize a design $\\rho$ together with the relaxed magnetization $\\vec{m}(T)$ on it." ] }, { "cell_type": "code", "execution_count": 7, "id": "b159efcd", "metadata": { "execution": { "iopub.execute_input": "2026-09-03T13:09:21.175463Z", "iopub.status.busy": "2026-09-03T13:09:21.175315Z", "iopub.status.idle": "2026-09-03T13:09:24.300757Z", "shell.execute_reply": "2026-09-03T13:09:24.299607Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_design(amps, title):\n", " m_T = np.asarray(llg.solve(ts, amps).ys[-1])\n", " rho = np.asarray(rho_func(amps))\n", " fig, ax = plt.subplots(figsize=(4.5, 4.5))\n", " ax.imshow(rho.T, origin=\"lower\", cmap=\"gray_r\", vmin=0, vmax=1, extent=(0, mesh.n[0], 0, mesh.n[1]))\n", " sl = slice(None, None, 2)\n", " X, Y = np.meshgrid((np.arange(mesh.n[0]) + 0.5)[sl], (np.arange(mesh.n[1]) + 0.5)[sl], indexing=\"ij\")\n", " ax.quiver(X, Y, m_T[sl, sl, 0], m_T[sl, sl, 1], color=\"tab:red\", scale=25)\n", " ax.set_title(title)\n", " plt.show()\n", "\n", "\n", "plot_design(state.rbf_amplitudes, \"initial shape and m(T)\")" ] }, { "cell_type": "markdown", "id": "f60fa4be", "metadata": {}, "source": [ "### Verify gradient flow\n", "Before optimizing, check that the gradient through the time integration is finite and non-zero. If this assert fires, the initial design has no interface inside the mesh (see above) or the state is not `float64`." ] }, { "cell_type": "code", "execution_count": 8, "id": "2b2a9fd8", "metadata": { "execution": { "iopub.execute_input": "2026-09-03T13:09:24.302949Z", "iopub.status.busy": "2026-09-03T13:09:24.302712Z", "iopub.status.idle": "2026-09-03T13:09:32.779945Z", "shell.execute_reply": "2026-09-03T13:09:32.778775Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "initial loss = 1.9999, max |dL/ds| = 2.68e-01\n" ] } ], "source": [ "loss, grad = grad_loss(state.rbf_amplitudes)\n", "assert np.all(np.isfinite(grad)) and np.abs(grad).max() > 0.0\n", "print(f\"initial loss = {float(loss):.4f}, max |dL/ds| = {np.abs(np.asarray(grad)).max():.2e}\")" ] }, { "cell_type": "markdown", "id": "d7cd2f3f", "metadata": {}, "source": [ "### Set up optimizer\n", "We use the AdaBelief optimizer with a learning rate of 0.01. The small learning rate matters here: adaptive optimizers keep moving the design at roughly the learning rate even after convergence, and larger rates can drift the converged design onto configurations where the relaxed magnetization flips between the degenerate $\\pm y$ equilibria, which shows up as spikes in the loss curve." ] }, { "cell_type": "code", "execution_count": 9, "id": "a91599b3", "metadata": { "execution": { "iopub.execute_input": "2026-09-03T13:09:32.781911Z", "iopub.status.busy": "2026-09-03T13:09:32.781745Z", "iopub.status.idle": "2026-09-03T13:09:32.810578Z", "shell.execute_reply": "2026-09-03T13:09:32.809707Z" } }, "outputs": [], "source": [ "optim = optax.adabelief(0.01)\n", "opt_state = optim.init(state.rbf_amplitudes)\n", "\n", "\n", "@eqx.filter_jit\n", "def make_step(amps, opt_state):\n", " loss, grads = grad_loss(amps)\n", " updates, opt_state = optim.update(grads, opt_state)\n", " amps = eqx.apply_updates(amps, updates)\n", " return loss, amps, opt_state" ] }, { "cell_type": "markdown", "id": "ddc76b28", "metadata": {}, "source": [ "### Perform optimization loop" ] }, { "cell_type": "code", "execution_count": 10, "id": "20f1f58c", "metadata": { "execution": { "iopub.execute_input": "2026-09-03T13:09:32.812299Z", "iopub.status.busy": "2026-09-03T13:09:32.812144Z", "iopub.status.idle": "2026-09-03T13:13:20.007801Z", "shell.execute_reply": "2026-09-03T13:13:20.006707Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|██████████| 200/200 [03:47<00:00, 1.14s/it]\n" ] } ], "source": [ "amps = state.rbf_amplitudes\n", "history = []\n", "for step in tqdm(range(200)):\n", " loss, amps, opt_state = make_step(amps, opt_state)\n", " history.append(float(loss))\n", "\n", "state.rbf_amplitudes = amps" ] }, { "cell_type": "markdown", "id": "e53cce2a", "metadata": {}, "source": [ "### Plot the solution\n", "The loss decreases smoothly; the shoulder around step 70 marks the transition of the design between shape configurations. Note that the loss measures a dynamical snapshot at $t = T$, and near configurations where the relaxation slows down it is a very sensitive function of the shape." ] }, { "cell_type": "code", "execution_count": 11, "id": "36bf9827", "metadata": { "execution": { "iopub.execute_input": "2026-09-03T13:13:20.010125Z", "iopub.status.busy": "2026-09-03T13:13:20.009933Z", "iopub.status.idle": "2026-09-03T13:13:20.096015Z", "shell.execute_reply": "2026-09-03T13:13:20.094662Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "final loss = 0.0094\n" ] } ], "source": [ "plt.figure(figsize=(5, 3.5))\n", "plt.plot(history)\n", "plt.xlabel(\"step\")\n", "plt.ylabel(\"loss\")\n", "plt.show()\n", "\n", "print(f\"final loss = {history[-1]:.4f}\")" ] }, { "cell_type": "markdown", "id": "d53c73a0", "metadata": {}, "source": [ "The optimized design splits the initial rectangle into two islands elongated along $y$ -- a topology change that a boundary-based shape optimization could not perform -- and the magnetization, driven by shape anisotropy alone, follows their long axis into the target direction." ] }, { "cell_type": "code", "execution_count": 12, "id": "043a269d", "metadata": { "execution": { "iopub.execute_input": "2026-09-03T13:13:20.098068Z", "iopub.status.busy": "2026-09-03T13:13:20.097852Z", "iopub.status.idle": "2026-09-03T13:13:20.416205Z", "shell.execute_reply": "2026-09-03T13:13:20.415261Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "rho-weighted (T) = (+0.069, +0.995, -0.000)\n" ] } ], "source": [ "plot_design(amps, \"final shape and m(T)\")\n", "\n", "m_T = np.asarray(llg.solve(ts, amps).ys[-1])\n", "rho = np.asarray(rho_func(amps))\n", "m_mean = (rho[..., None] * m_T).sum((0, 1)) / rho.sum()\n", "print(f\"rho-weighted (T) = ({m_mean[0]:+.3f}, {m_mean[1]:+.3f}, {m_mean[2]:+.3f})\")" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.13.4" } }, "nbformat": 4, "nbformat_minor": 5 }