{ "cells": [ { "cell_type": "markdown", "id": "f0bcc576", "metadata": {}, "source": [ "# Shape optimization with a level-set parameterization (PyTorch 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": "0ddf72fc", "metadata": {}, "source": [ "### Import libraries\n", "Import libraries and set the backend to PyTorch. The default `float32` precision is sufficient here: on the torch backend the gradients through the LLG time integration flow normally under `float32` (on the JAX backend they do not -- see the JAX version of this example, which requires `float64`)." ] }, { "cell_type": "code", "execution_count": 1, "id": "5791a37d", "metadata": { "execution": { "iopub.execute_input": "2026-09-03T13:18:20.335575Z", "iopub.status.busy": "2026-09-03T13:18:20.335416Z", "iopub.status.idle": "2026-09-03T13:18:25.533743Z", "shell.execute_reply": "2026-09-03T13:18:25.533159Z" } }, "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 15:18:24 NeuralMag:INFO \u001b[1;37;32m[NeuralMag] Version 1.0.0\u001b[0m\n", "2026-09-03 15:18:25 NeuralMag:INFO \u001b[1;37;32m[NeuralMag] Backend set to 'torch'.\u001b[0m\n", "2026-09-03 15:18:25 NeuralMag:INFO \u001b[1;37;32m[NeuralMag] Set default device to 'cpu'.\u001b[0m\n" ] } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import torch\n", "from tqdm import tqdm\n", "\n", "import neuralmag as nm\n", "\n", "nm.config.backend = \"torch\"\n", "nm.config.device = \"cpu\"" ] }, { "cell_type": "markdown", "id": "fda7c568", "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": "ebc0432a", "metadata": { "execution": { "iopub.execute_input": "2026-09-03T13:18:25.535574Z", "iopub.status.busy": "2026-09-03T13:18:25.535353Z", "iopub.status.idle": "2026-09-03T13:18:25.555840Z", "shell.execute_reply": "2026-09-03T13:18:25.555311Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "2026-09-03 15:18:25 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 15:18:25 NeuralMag:INFO \u001b[1;37;32m[NeuralMag] Set default dtype to 'float32'.\u001b[0m\n", "2026-09-03 15:18:25 NeuralMag:INFO \u001b[1;37;32m[State] Running on device: cpu (dtype = torch.float32, backend = torch)\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": "457cbf58", "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": "1089ffbe", "metadata": { "execution": { "iopub.execute_input": "2026-09-03T13:18:25.557120Z", "iopub.status.busy": "2026-09-03T13:18:25.556987Z", "iopub.status.idle": "2026-09-03T13:18:25.585139Z", "shell.execute_reply": "2026-09-03T13:18:25.584606Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "2026-09-03 15:18:25 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": "921b3ad3", "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": "419a617c", "metadata": { "execution": { "iopub.execute_input": "2026-09-03T13:18:25.586492Z", "iopub.status.busy": "2026-09-03T13:18:25.586362Z", "iopub.status.idle": "2026-09-03T13:18:25.777957Z", "shell.execute_reply": "2026-09-03T13:18:25.777415Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "2026-09-03 15:18:25 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 15:18:25 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 15:18:25 NeuralMag:INFO \u001b[1;37;32m[DemagField]: Set up demag tensor\u001b[0m\n", "2026-09-03 15:18:25 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": "ffdaaa25", "metadata": {}, "source": [ "### Set up LLGSolver\n", "The RBF amplitudes are registered as solver parameters in order to allow for efficient gradient computation through the time integration. On the PyTorch backend the solver is an `nn.Module` and the design variable becomes an `nn.Parameter` owned by it, so `llg.solve(ts)` takes no extra arguments and gradients arrive via `loss.backward()`." ] }, { "cell_type": "code", "execution_count": 5, "id": "95800c91", "metadata": { "execution": { "iopub.execute_input": "2026-09-03T13:18:25.779611Z", "iopub.status.busy": "2026-09-03T13:18:25.779473Z", "iopub.status.idle": "2026-09-03T13:18:25.782811Z", "shell.execute_reply": "2026-09-03T13:18:25.782343Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "2026-09-03 15:18:25 NeuralMag:INFO \u001b[1;37;32m[LLGSolverTorch] Initialize RHS function\u001b[0m\n" ] } ], "source": [ "llg = nm.LLGSolver(state, parameters=[\"rbf_amplitudes\"])\n", "amps = dict(llg.named_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": "45d1aa08", "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." ] }, { "cell_type": "code", "execution_count": 6, "id": "330779b5", "metadata": { "execution": { "iopub.execute_input": "2026-09-03T13:18:25.783963Z", "iopub.status.busy": "2026-09-03T13:18:25.783838Z", "iopub.status.idle": "2026-09-03T13:18:25.786121Z", "shell.execute_reply": "2026-09-03T13:18:25.785629Z" } }, "outputs": [], "source": [ "def loss_fn():\n", " m_T = llg.solve(ts)[-1]\n", " rho = rho_func(amps)\n", " return (rho * ((m_T - m_target) ** 2).sum(-1)).sum() / rho.sum()" ] }, { "cell_type": "markdown", "id": "fefb1b60", "metadata": {}, "source": [ "### Define plot function\n", "Visualize the current design $\\rho$ together with the relaxed magnetization $\\vec{m}(T)$ on it." ] }, { "cell_type": "code", "execution_count": 7, "id": "25da4a1d", "metadata": { "execution": { "iopub.execute_input": "2026-09-03T13:18:25.787217Z", "iopub.status.busy": "2026-09-03T13:18:25.787096Z", "iopub.status.idle": "2026-09-03T13:18:27.881764Z", "shell.execute_reply": "2026-09-03T13:18:27.881139Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_design(title):\n", " with torch.no_grad():\n", " m_T = np.asarray(llg.solve(ts)[-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", " return m_T, rho\n", "\n", "\n", "_ = plot_design(\"initial shape and m(T)\")" ] }, { "cell_type": "markdown", "id": "8716da5e", "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)." ] }, { "cell_type": "code", "execution_count": 8, "id": "6b1e683e", "metadata": { "execution": { "iopub.execute_input": "2026-09-03T13:18:27.883366Z", "iopub.status.busy": "2026-09-03T13:18:27.883227Z", "iopub.status.idle": "2026-09-03T13:18:32.329432Z", "shell.execute_reply": "2026-09-03T13:18:32.328756Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "initial loss = 1.9999, max |dL/ds| = 2.68e-01\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/tmp/ipykernel_1478461/1489557022.py:5: UserWarning: Converting a tensor with requires_grad=True to a scalar may lead to unexpected behavior.\n", "Consider using tensor.detach() first. (Triggered internally at /__w/pytorch/pytorch/torch/csrc/autograd/generated/python_variable_methods.cpp:820.)\n", " print(f\"initial loss = {float(loss):.4f}, max |dL/ds| = {np.abs(grad).max():.2e}\")\n" ] } ], "source": [ "loss = loss_fn()\n", "loss.backward()\n", "grad = np.asarray(amps.grad)\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(grad).max():.2e}\")" ] }, { "cell_type": "markdown", "id": "65b5a20e", "metadata": {}, "source": [ "### Set up optimizer\n", "We use the Adam 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": "92daa4ea", "metadata": { "execution": { "iopub.execute_input": "2026-09-03T13:18:32.331151Z", "iopub.status.busy": "2026-09-03T13:18:32.331013Z", "iopub.status.idle": "2026-09-03T13:18:33.482285Z", "shell.execute_reply": "2026-09-03T13:18:33.481678Z" } }, "outputs": [], "source": [ "optimizer = torch.optim.Adam([amps], lr=0.01)" ] }, { "cell_type": "markdown", "id": "e5afa485", "metadata": {}, "source": [ "### Perform optimization loop" ] }, { "cell_type": "code", "execution_count": 10, "id": "5a028fff", "metadata": { "execution": { "iopub.execute_input": "2026-09-03T13:18:33.484328Z", "iopub.status.busy": "2026-09-03T13:18:33.484191Z", "iopub.status.idle": "2026-09-03T13:34:43.590041Z", "shell.execute_reply": "2026-09-03T13:34:43.589519Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|██████████| 200/200 [16:10<00:00, 4.85s/it]\n" ] } ], "source": [ "history = []\n", "for step in tqdm(range(200)):\n", " optimizer.zero_grad()\n", " loss = loss_fn()\n", " loss.backward()\n", " optimizer.step()\n", " history.append(float(loss))\n", "\n", "state.rbf_amplitudes = amps.detach().clone()" ] }, { "cell_type": "markdown", "id": "24914c5f", "metadata": {}, "source": [ "### Plot the solution\n", "The loss decreases smoothly; the shoulders mark transitions 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": "ccc6e682", "metadata": { "execution": { "iopub.execute_input": "2026-09-03T13:34:43.592411Z", "iopub.status.busy": "2026-09-03T13:34:43.592267Z", "iopub.status.idle": "2026-09-03T13:34:43.671638Z", "shell.execute_reply": "2026-09-03T13:34:43.670992Z" } }, "outputs": [ { "data": { "image/png": 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qxRG8/O0xZKk1UpdHRLWIRQSqEAIajQYGg+GBfXU6HTQajclSVFRUbv+K7JNqN5lMht5hvtg5JRpjHg2CXAb8dOo6eszbi9UHLkNv4F0PInp4kgbqzZs3MWfOHDRp0gQODg7Yt2/fA7eZNGkSnJyc4O7ublwiIyNL9YuLi0P9+vVha2uL8PBw7Nmzpzo+AlkRZ6UN3usfik2THkXrAHfkaXV4P+EMhizcj9/vjgwmIqoqSQN10aJFyM3NxapVqyq13eDBg03OUJOTk03WL168GLNnz8aaNWugUqkwZMgQ9O/fH5cuXTJn+WSlWvq54ceJXTBzUBhclDY4maHCwM9/w/yd53m2SkRVJmmgvv/++/joo4/QpEmTSm97v0u5n3zyCcaMGYOePXvC2dkZ06dPR7169bB48eKHKZdqEYVchuciA7H79Wj0b9UABgF8ujsFzy07hJw75d9CICIqj0XcQ62srVu3QqlUwtPTEwMHDkRKSopxXXZ2NlJSUhAdHW1sk8lkiI6OxoEDB6QolyyYj6s9Ph/eFvOHtYajnQJJqdkYvHA/Lt7Ml7o0IrIyVheoISEhSEhIQH5+PpKTkyGEQHR0NHJzcwEAmZmZAABvb2+T7Xx8fIzryqLVaqFWq00WqjsGR/gj4eUo+Hs44Ep2Af61KAlnr/FngIgqzuoCdfLkyejVqxeUSiWCgoKwZs0a3L59G/Hx8Sb9/nlJ2GAw3Hf6ubi4OLi5uRmXgICAaqmfLFez+i7Y8FIUWvm7IbegGMOXHsSZaxysREQVY3WB+k+urq7w9/dHamoqAKBBgwYAgKws04f3s7Ky4OvrW+5+YmNjoVKpjEt6enr1FU0Wy9tFia/HdELrAHfcLijGqBVHcF1VKHVZRGQFLD5QdTrdfZ8zzcnJQVpaGvz9/QEAHh4eCA0NRWJiorGPwWBAYmIioqKiyt2PUqmEq6uryUJ1k5uDLb4e0xHN67vgZp4WY1cdRUGRTuqyiMjCSRqoer0eGo0GWq0WAFBUVASNRgOd7q9fXhMmTEDbtm0BlNzn7NevH/bt24fs7GwcP34cQ4cOhYeHB0aMGGHcZtq0aVi+fDl++OEHXLt2DVOmTEF+fj4mTpxYsx+QrJarvS2WPt8eXk52OHNNjRmbzkpdEhFZOEkD9dtvv4W7uzvCwsKgVCoxcOBAuLu7Y86cOcY+tra2UCpLXhatVCoxdepUzJo1CyEhIRg2bBiCgoJw5MgReHl5GbcZOXIk5s2bh9jYWLRo0QJHjx7Fzp07jWexRBUR4OmIL55tC5kMiD+azjmAiei++LaZcvBtM3TPjM1nsGL/ZTRws8eO1x6Dq72t1CURUQ3h22aIzOjN3iEI9HLEdZUGi39JlbocIrJQDFSiB3CwU+CdJ0MBAMv3X+JbaoioTAxUogro2cIHbRu5Q1NswKe7Ux68ARHVOQxUogqQyWSY1icEAPDdkXSk5xRIXBERWRoGKlEFdWrihahgL+gNAst+45uLiMgUA5WoEiZENwUAxB9JRy7fSkNEf8NAJaqER4PrIayhKwqL9Vh94IrU5RCRBWGgElWCTCbD+LtnqasOXEZhkV7iiojIUjBQiSqpX0tfBHg6IOdOEb5P5ksUiKgEA5WokmwUcozr2gQAsGTfRej0hgdsQUR1AQOVqAqebhcATyc7ZOQWYuvvN6Quh4gsAAOVqAoc7BR4PjIQALD4l1RwSmwiYqASVdHIyMZwsFXg7HU1frtwS+pyiEhiDFSiKvJwssOwDgEAgMV7OWk+UV3HQCV6CGO7BkEhl2H/hWycyrgtdTlEJCEGKtFD8PdwxMDWDQEAC3Zx0nyiuoyBSvSQ/tOjGRRyGfb8mYXkKzlSl0NEEmGgEj2koHpOeLqdPwBg7o5zHPFLVEcxUInM4JUezWCnkOPgxRzsv5AtdTlEJAGLCFQhBDQaDQyGis84c7+zAJ1OB41GY7IUFfHNIFR9/NwdMLxTIwDA3J95lkpUF0kaqDdv3sScOXPQpEkTODg4YN++fQ/cZseOHejVqxfc3Nzg5uaGJ598En/88YdJn0mTJsHJyQnu7u7GJTIysro+BhEA4OXuwXCwVeBk+m3sPJspdTlEVMMkDdRFixYhNzcXq1atqlB/vV6P+fPn46233sK1a9eQmpoKJycn9OrVC2q12qTv4MGDTc5Qk5OTq+MjEBl5uygxOioQADDv5/PQG3iWSlSX2Ej5h7///vsAgIyMjAr1VygU2L59u/F7Z2dnzJs3D40aNcKhQ4fQq1cvk/4GgwFyuUVc1aY6YvxjTfH1wSs4l5mHLaeuYVAbP6lLIqIaYvVpc/36dQCAh4eHSfvWrVuhVCrh6emJgQMHIiWFzwhS9XNztMX4x0reRDN/53kU8000RHWGVQdqUVERJk+ejI4dO6Jdu3bG9pCQECQkJCA/Px/JyckQQiA6Ohq5ubnl7kur1UKtVpssRFUxOioIXk52uJxdgB+SK3b1hYisn9UGqsFgwKhRo5CWlob4+HjIZDLjusmTJ6NXr15QKpUICgrCmjVrcPv2bcTHx5e7v7i4OONAJzc3NwQEBNTEx6BayElpg4ndmgIAPtudAk2xXuKKiKgmWGWg3gvTX375BYmJiQgMDLxvf1dXV/j7+yM1tfwJzGNjY6FSqYxLenq6maumumRE58bwdbXHNZUG3x5Kk7ocIqoBFh+oOp3O5BlSg8GAF154Abt27UJiYiKaNWv2wH3k5OQgLS0N/v7+5fZRKpVwdXU1WYiqyt5Wgf/0KPnZXPjLBRQU6SSuiIiqm6SBqtfrodFooNVqAZTcE9VoNNDp/vrlM2HCBLRt2xZAyWQO48aNw7Zt27B9+3Y0btzY+FiMXl9yWU2r1aJfv37Yt28fsrOzcfz4cQwdOhQeHh4YMWJEzX9IqrOebu+Pxl6OuJVfhJVJl6Uuh4iqmaSB+u2338Ld3R1hYWFQKpUYOHAg3N3dMWfOHGMfW1tbKJVKACVnmmvWrIFKpULHjh1NJm74+uuvAZScaU6dOhWzZs1CSEgIhg0bhqCgIBw5cgReXl6SfE6qm2wVcrx69yz1q30XcUfLs1Si2kwmOEdamdRqNdzc3KBSqXj5l6pMpzeg5yd7cTm7ANP6hBgHKxGRdahMFlj8PVQia2ajkOOVx++epf7Ks1Si2oyBSlTNBrVpiEAvR+TcKcI3B69IXQ4RVRMGKlE1s1HI8XL3YADAkn0XOeKXqJZioBLVgMERfmjk6YhsnqUS1VoMVKIaYKOQY9LjJWepX+7lvVSi2oiBSlRDBkf4IdCr5Cz1q18vSl0OEZkZA5Wohtgq5JjauzmAknupN/O0EldERObEQCWqQU+GN0BrfzcUFOnx6e7zUpdDRGbEQCWqQTKZDLH9WgAAvj2Uht+vqiSuiIjMhYFKVMM6N/HCgNYNYRDAOxt/h8HAycqIaoMqBWpWVhY+//xz4/dLlixBcHAwevfujevXr5utOKLa6t0nW8BZaYOT6bex5jBf70ZUG1QpUKdOnWqcaP769et49dVXMXr0aNjZ2WHKlClmLZCoNqrvao+pTzwCAIjb+gfScwokroiIHlaVAnX79u3o27ev8b979OiBd955B19++SV2795t1gKJaquRkYHoGOSJgiI9pn5/kpd+iaxclQK1qKjI+A7TXbt2oWfPngAAJycnk5eBE1H55HIZ/ju0NRztFDh0KYfvTCWyclUK1K5du2LixIn47LPPsGHDBgwYMAAAcPDgQURGRpq1QKLarJGXI96+O+r34x1/4uLNfIkrIqKqqlKgfvHFFyguLsbSpUsxf/58NG1a8o7HhQsX4r333jNrgUS13bOdGqFrs3rQFBvw+vcnoeelXyKrxBeMl4MvGKeadO12IXrP34c8rY4vIieyINX+gnE+NkNkXg3dHfD+gFAAwPyd53HuRp7EFRFRZfGxGSILMbSdP3qE+KBIb8Br8SdQpDNIXRIRVYJFPDYjhIBGo4HBULlfIBXpX9l9EklFJpMhbkg4PBxtcfa6GvN2npO6JCKqBEkfm7l58ybmzJmDJk2awMHBAfv27avQdnFxcahfvz5sbW0RHh6OPXv2VKkPkaXxcbXHnH+1AlDyRpqkC7ckroiIKkrSx2YWLVqE3NxcrFq1qsLbLF68GLNnz8aaNWugUqkwZMgQ9O/fH5cuXapUHyJL1TvMF//u2AhCAFPWncTtAj7bTWQVRBVcuXJF9O/fX4SHh4vFixcb2wcOHCj2799f6f2lp6cLACIxMfGBfZs1ayZeffVV4/cGg0EEBASIN998s1J9HkSlUgkAQqVSVXgbInO5oy0W3ecmisbTtogJXx8VBoNB6pKI6qTKZIFNVUK4UaNG2Lx5c6n2hISEh0v3B8jOzkZKSgqio6ONbTKZDNHR0Thw4ECF+xBZOkc7Gyx4pg2GLEzCtt9v4NvDaXi2U2OpyyKi+3jo17cVFBSgoKBmJvbOzMwEAHh7e5u0+/j4GNdVpE9ZtFot1Gq1yUIkpVb+7pjauzkAYPqmM0i+kitxRUR0P1UKVCEEFi1ahMDAQDg5OcHJyQmBgYFYtGgRRA3ME/HPkbsGgwEymazSff4uLi4Obm5uxiUgIMB8BRNV0fjHmqBvS18U6wVeWpOMrDyN1CURUTmqFKgff/wxYmNjMWrUKGzbtg3bt2/HqFGj8NZbb+Hjjz82d41GDRo0AFAyscTfZWVlwdfXt8J9yhIbGwuVSmVc0tPTzVk6UZXIZDLMfbo1mvk4I1OtxctrjvH5VCILVeW5fNeuXYvp06ejT58+6N27N6ZPn47vvvsOCxcuNGuBOp3O+CiOh4cHQkNDkZiYaFxvMBiQmJiIqKioCvcpi1KphKurq8lCZAmclTb48rl2cFHa4MjlXMzcclbqkoioDFUK1Bs3bpQZTlFRUZWaelCv10Oj0RifaS0qKoJGo4FOpzP2mTBhAtq2bWv8ftq0aVi+fDl++OEHXLt2DVOmTEF+fj4mTpxYqT5E1qSJtzMWPNMGAPD1wStY+utFaQsiolKqFKjBwcH4/vvvS7XHx8cjODi4wvv59ttv4e7ujrCwMCiVSgwcOBDu7u6YM2eOsY+trS2USqXx+5EjR2LevHmIjY1FixYtcPToUezcuRP+/v6V6kNkbXq0qI+3+4UAAGb99AcSTlyVuCIi+rsqvW0mPj4eI0aMwKBBg9CxY0cAwKFDh5CQkIA1a9Zg2LBhZi+0pvFtM2SJhBCYsfksViZdhkIuw/xhbTCwdUOpyyKqtSqTBVV6DnXYsGHw9/fH3Llz8dVXX0EmkyE0NBT79u1Dly5dqlQ0ET2YTCbDe/1DcUerw/fJGZj83XEIITCojZ/UpRHVeXwfajl4hkqWzGAQiP3xNOKPpkMuA+bFtMbgCN7SIDK3an8fKhFJSy4veTPNMx0CYLg75+93h9OkLouoTqvwJd/KDOjJyMioUjFEVHFyuQyzB4dDIZdhzaE0vPXjaag1xXjxsaZSl0ZUJ1U4UGfNmlWddRBRFcjlMsx6qiWc7W3w5d6LmL31T6gKizH1ieb3nRmMiMyP91DLwXuoZG0W/nIBH28veSn5c50bY8bAMMjlDFWih8F7qER10EvdgjHzqZaQyUomf5iy7gSK9ZymkKimMFCJapHnOjfGgmFtYCOXYeOJa5j4TTI0xXqpyyKqExioRLXMoDZ+WDKyHZQ2cuz6IwujVhxGvlb34A2J6KEwUIlqocdD6mPVCx3hrLTBwYs5GP7VQeTcKZK6LKJajYFKVEt1buKFteM6w8PRFqcyVBj25QHcUPF9qkTVhYFKVIuF+7th3fhI+LraIyUrH0MXJ+FK9h2pyyKqlRioRLVcs/ou+H5CJBp7OSIjtxDDvjyIjNwCqcsiqnUYqER1QICnI76fEIlgH2fcUGvw3LLDuJmnlbosolqFgUpUR/i42OObMZ3g5+6AS7fu4Pnlh6EqLJa6LKJag4FKVIf4utljzdhOqOesxNnraoxddQSFRXxOlcgcGKhEdUxgPSesfqEjXOxtcORyLqZ+fxKcgZTo4TFQieqg0IauWDqyPWwVMvx0+jo+33NB6pKIrB4DlaiO6tTECzMHtQQAzNt5Htt/vyFxRUTWzWIC1WCo2CTeWq0WGo2m1KLT/TW1mk6nK7W+qIizxBD90zMdG2FUl0AAwJR1J/DHdbW0BRFZMckDNS4uDvXr14etrS3Cw8OxZ8+e+/b38/ODu7u7yeLg4IDXX3/d2GfSpElwcnIy6RMZGVndH4XIKr37ZAs8GlwPBUV6jFt9FLmcopCoSiQN1MWLF2P27NlYs2YNVCoVhgwZgv79++PSpUvlbnPr1i2TM8/NmzcDAGJiYkz6DR482KRfcnJytX4WImtlo5Dj8+ERaORZMvHD5PgT0Bs4SImosiQN1E8++QRjxoxBz5494ezsjOnTp6NevXpYvHhxhfexbNkytGjRAlFRUaXWVfQyMlFd5+5oh8Uj2sHeVo6952/is90pUpdEZHUkC9Ts7GykpKQgOjra2CaTyRAdHY0DBw5UaB85OTnYuHEjxo0bV2rd1q1boVQq4enpiYEDByIlhb8giO4ntKErZg8OBwB8ujsFe/7MlLgiIusiWaBmZpb8ZfX29jZp9/HxMa57kG+++QYAMHLkSJP2kJAQJCQkID8/H8nJyRBCIDo6Grm5ueXuS6vVQq1WmyxEdc2Qtv54rnNjAMDk704gLZtz/hJVlOSDkv55WdZgMEAmk1Vo22XLlmHw4MHw8vIyaZ88eTJ69eoFpVKJoKAgrFmzBrdv30Z8fHy5+4qLi4Obm5txCQgIqPyHIaoF3usfiohG7lBrdBj/TTJnUiKqIMkCtUGDBgCArKwsk/asrCz4+vo+cPujR4/i1KlTZV7u/SdXV1f4+/sjNTW13D6xsbFQqVTGJT09/YH7JaqN7GzkWPhsW3g52eGP62q8s/E0Z1IiqgDJAtXDwwOhoaFITEw0thkMBiQmJpoMMNLpdGU+Q7ps2TIEBweje/fuD/yzcnJykJaWBn9//3L7KJVKuLq6mixEdVUDNwf8b3gE5DLgx2NXseZQmtQlEVk8SS/5Tps2DcuXL8cPP/yAa9euYcqUKcjPz8fEiRONfSZMmIC2bduabFdYWIi1a9di7NixpS4Pa7Va9OvXD/v27UN2djaOHz+OoUOHwsPDAyNGjKiRz0VUG3RpWg/T+oQAAGZsPoPjaeWPQSAiwEbKP3zkyJHIz89HbGwsMjMzER4ejp07d5qcSdra2kKpVJpst3HjRuh0OowaNarUPpVKJaZOnYpZs2bh+PHj8PDwQNeuXbF69epS91qJ6P5efKwJjqfdxvYzNzDxm2PYNCkKPq72UpdFZJFkgjdHyqRWq+Hm5gaVSsXLv1Sn5WmK8dQX+5F68w7C/dwQP74zHO0k/bc4UY2pTBZIPsqXiCybi70tlo/qAE8nO5y+qsKr33EmJaKyMFCJ6IEaezlhyXPtYKeQY+fZTMRt/UPqkogsDgOViCqkfaAn5j7dCgCw9LdLWLm//Dm3ieoiBioRVdigNn54vdcjAIDpm89ifXKGxBURWQ4GKhFVyqTHgzE6KhAA8Ob6k/jp1HVpCyKyEAxUIqoUmUyG9/uH4pkOATAI4NXvjnMifSIwUImoCmQyGT4cHI6BrRtCZxCY8M0x7DzLUKW6jYFKRFWikMswL6Y1+oT5okhnwIRvkvHjMd5TpbqLgUpEVWarkOPz4RH4V1t/6A0CU9adxPLfOPqX6iYGKhE9FBuFHHOHtjIOVPq/LWfx8fY/YeDkD1THMFCJ6KHJ5SUDlV7rWfJIzcJfUjFp7TG+S5XqFAYqEZmFTCbDqz2bYe7QVrBVyLD19A3EfHkAmWqN1KUR1QgGKhGZ1dPtA7BmbGd4ONri9FUVBn7+G36/qpK6LKJqx0AlIrPrGOSJjS9HIdjHGZlqLZ5efADbf+cEEFS7MVCJqFo09nLCjy91Qddm9VBYrMeEb45h4S8XwDdGUm3FQCWiauNqb4sVozrg+cjGAICPt5/DG+tPoVhvkLgyIvNjoBJRtbJRyDFjUEv836AwKOQyrE/OwAsrjyBPUyx1aURmxUAlohoxMjIQS0e2h4OtAr+m3ELMlwdxQ8URwFR7MFCJqMZ0D/FB/PjOqOesxB/X1RiycD9Sb+ZLXRaRWVhdoBoMBuh0OpNFr+fD40TWopW/Oza81AVNvZ1wTaXBM0sOIiUzT+qyiB6a5IE6d+5c+Pn5wdbWFhEREdi7d+99+7/00kuws7ODvb29cWnXrt1D75eIak6ApyPWjY9EiwauuJmnxTNLDuLPG2qpyyJ6KJIG6pIlSzBjxgwsW7YMt27dQr9+/dCvXz9cvnz5vtsNGTLE5Az1xIkTZtkvEdUcL2cl1o7rhJZ+rsi+U4R/LznICSDIqkkaqPPmzcOYMWPQp08fuLm5YdasWfD09MTixYstcr9EZF7ujnZYM7YzWge4I7egGM8tO4QLWbz8S9ZJskDNycnB+fPnER0dbWyTyWTo1q0bkpKS7rvttm3boFQq4e3tjSFDhiA1NdUs+yWimufmYItvxnREa3835BYUY8TSw8jILZC6LKJKkyxQb9y4AQDw9vY2affx8UFmZma52z3yyCNYv349cnNzkZSUBI1Gg+joaNy+ffuh9qvVaqFWq00WIqoZLva2WDm6I5r5OOOGWoPnlh3GzTyt1GURVYrkg5L+yWAwQCaTlbt+ypQp6Nu3LxwdHdGsWTOsXbsW2dnZiI+Pf6j9xsXFwc3NzbgEBARU+TMQUeV5ONnh6zGd4OfugEu37mDk8sNQc/IHsiKSBWqDBg0AAFlZWSbtN2/ehK+vb4X3cy/8Lly48FD7jY2NhUqlMi7p6ekVroGIzMPXzR5rxnYyPqf60jfHOE0hWQ3JAtXDwwMtWrRAYmKisU0IgcTERHTp0sXYZjAY7vucaW5uLtLS0uDn51ep/f6TUqmEq6uryUJENS+wnhNWju4ARzsFfrtwC+8n/M4J9ckqSHrJ94033sDy5cuRkJCArKwsTJ06FWq1GhMnTjT2efHFF9G6dWsAJfc5BwwYgKSkJKhUKpw+fRoxMTFwc3PDs88+W6n9EpHlaunnhs+eiYBMBqw9nI6vfr0odUlED2Qj5R8+evRo5OXl4bXXXkNmZibCw8Px888/m9y/VCgUsLEpKVOpVGLSpEl49913cfz4cXh4eKBr165YtmyZySCkiuyXiCxbz9D6ePfJUMzcchZx2/5EI08n9GlZ8dtBRDVNJngtpUxqtRpubm5QqVS8/EskESEE3k84g68PXoGDrQIbX45Cc18XqcuiOqQyWWBxo3yJiO6RyWT4YEAoHg0ueUn5+K+PQlXIkb9kmRioRGTRbBRy/O/fEfBzd8Dl7AJM/u44DAZeWCPLw0AlIovn4WSHL59rB6WNHInnbuLT3SlSl0RUCgOViKxCSz83zB4cDgD4dHcK9vxZ/sxnRFJgoBKR1fhXO388H9kYAPD6upO4riqUuCKivzBQiciqvP1kC7T0c0VuQTFe/e4EdJxJiSwEA5WIrIrSRoHP/90WzkobHL6Ug8/2XJC6JCIADFQiskKB9Zzw4eCWAID/7UlB0oVbEldExEAlIis1qI0fhrUPgBDA5PgTyL1TJHVJVMcxUInIak0fGIam3k7IytPinY2nOYk+SYqBSkRWy8FOgQXDImAjl2Hr6RvYeOKq1CVRHcZAJSKrFu7vhld7NAMAvJ9wBldv81EakgYDlYis3sRuTRHRyB15Gh2mrjvJqQlJEgxUIrJ6Ngo55se0gYOtAgcuZmNF0mWpS6I6iIFKRLVCYD0nvNu/BQDgo+1/4nxmnsQVUV3DQCWiWmN4x0bo3twbRToDXos/gSIdZ1GimsNAJaJaQyaT4aN/tYKHoy3OXFPjM76VhmoQA5WIahUfV3vjW2kW/nIBx9JyJa6I6goGKhHVOn3DG+CpNg1hEMDUdSdRWKSXuiSqA2ploBoMBuh0OpNFr+dfKKK6ZMbAlvB1tcfFW3fw0fY/pS6H6gDJA3Xu3Lnw8/ODra0tIiIisHfv3vv23717N/r27Qt3d3d4eXlh0KBBOHfunEmfl156CXZ2drC3tzcu7dq1q86PQUQWxs3RFh8PbQUAWJl0Gb+lcAJ9ql6SBuqSJUswY8YMLFu2DLdu3UK/fv3Qr18/XL58ucz+er0ecXFxmDx5Mq5cuYIzZ87AxsYGvXr1Ql6e6RD5IUOGmJyhnjhxovo/EBFZlMce8caIzo0AAG+sPwlVYbHEFVFtJmmgzps3D2PGjEGfPn3g5uaGWbNmwdPTE4sXLy6zv0KhwK5du9C7d2+4ubnB19cXCxYsQHp6Og4ePFjD1RORNXi7Xws09nLEdZUGMzafkbocqsUkC9ScnBycP38e0dHRxjaZTIZu3bohKSmpwvvJzMwEALi7u5u0b9u2DUqlEt7e3hgyZAhSU1PNUjcRWRdHOxt8EtMachnw47Gr2P77DalLolpKskC9caPkh9rb29uk3cfHxxiSD1JcXIzXXnsN7du3N7lH+sgjj2D9+vXIzc1FUlISNBoNoqOjcfv27XL3pdVqoVarTRYiqh3aNfbE+OimAIB3NpzGrXytxBVRbST5oKR/MhgMkMlkFer3wgsvIDU1FfHx8ZDL//ooU6ZMQd++feHo6IhmzZph7dq1yM7ORnx8fLn7i4uLg5ubm3EJCAgwy+chIsswuWczhPi6IPtOEWJ/5LtTyfwkC9QGDRoAALKyskzab968CV9f3/tuK4TA2LFjsWvXLuzZswdNmjS5b/97AXnhwoVy+8TGxkKlUhmX9PT0Cn4SIrIGShsFPolpA1uFDDvPZmLdUf4dJ/OSLFA9PDzQokULJCYmGtuEEEhMTESXLl2MbQaDweQZ0nthunXrVuzZswchISEP/LNyc3ORlpYGPz+/cvsolUq4urqaLERUu4Q2dMWUXs0BANM3ncWFLE6gT+Yj6SXfN954A8uXL0dCQgKysrIwdepUqNVqTJw40djnxRdfROvWrQGUhOmECROwZcsW7Ny5E82aNTM+FnPv8o1Wq8WAAQOQlJQElUqF06dPIyYmBm5ubnj22Wcl+ZxEZDnGP9YEUcFeKCzW45W1J6Ap5qQvZB6SBuro0aMxZ84cvPbaawgKCsL+/fvx888/m9y/VCgUsLGxAVAyMnjZsmXIzs5GRESEycQNK1asAFBypjlp0iS8++67CAwMxKBBg9CwYUMcOXKk1AAoIqp75HIZ5se0gZeTHf64rsacbZxFicxDJnhnvkxqtRpubm5QqVS8/EtUCyWey8LoFUcAAEtHtkfP0PoSV0SWqDJZYHGjfImIakL35j4Y+2gQAOD1708iLbtA4orI2jFQiajOerNPCNoEuENVWIwXvz6KgiKd1CWRFWOgElGdZWcjx+IR7VDPWYk/b+ThzfWn+HwqVRkDlYjqNF83eywa0RY2chm2nLqOJfsuSl0SWSkGKhHVeR0CPfHBgFAAwEfb/0TiuawHbEFUGgOViAjAiM6NMax9AAwCeHnNMZzOUEldElkZBioREUredjXzqZaICvZCQZEeo1cewaVbd6Qui6wIA5WI6K57g5RaNHDFrXwthn91EOk5fJyGKoaBSkT0Ny72tlj9Qkc09XbCdZUGzyw5yDNVqhAGKhHRP3i7KPHtuM4IqueEq7cL8fTiJPx+lfdU6f4YqEREZajvao914yMR2sAVt/KL8PTiA/jp1HWpyyILxkAlIiqHt4sS343vjK7N6qGwWI+Xvz2GmVvO8g01VCYGKhHRfbja22LFqA4Y17Vk3t9lv13CoM/3I/lKrsSVkaVhoBIRPYCNQo53ngzFsufbw8vJDucy8/CvRUl4fd1JjgImI76+rRx8fRsRlSU7X4s52/7E98kZAAAbuQyD2vjh3x0D0K6xB2QymcQVkjlVJgsYqOVgoBLR/RxPy8UnO8/j15RbxrZmPs4Y1iEAvULro7GXk4TVkbkwUM2AgUpEFXEsLRdrD6Vhy6nrKPzbYKVAL0dEP+KNzk28EO7vBj93B569WiEGqhkwUImoMtSaYmw6cQ2bT15D8pVc6Aymv1o9nezQ0s8NTeo5obGXIwK9Sr76ezjCzobDWSwVA9UMGKhEVFV5mmIcSM3GvpSbOJ52G+du5JUK2HvkMqCesxLeLiXLvf/2crKDi70NXO1t4WJvW/LfDiVfnZU2UNrIecZbAxioZsBAJSJz0RTr8eeNPJy9psaVnDu4cqsAl7Pv4Ep2gcll4sqQyQAHWwXsbRV3v8rhYKeAvY2i5OvddUobOWwVctgpZLC7+9+2CjnsbOSwU8hhq5DB9m678m/rbe/2t/tbf1uFDDZyOWz+9tVWLodCIYONXAZbhRwKee0K+cpkgU0N1VSuuXPnYsGCBcjKykLLli2xYMECREdHP/Q2VdkvEVF1sLdVoE2AO9oEuJu0CyFwM0+LrDwtbuZpcTP/7tc8LXILipCn0UFdWFzyVVPyNV+ru7stUFCkR0GRZU0yIZOVjHz+K3hlsFHIYSuXQXE3gG0Updf/vZ/NP4P7btu9wLYx2c/ftr+3D4UMCnnJ12AfZ4Q1dKuRzy5poC5ZsgQzZszA+vXrERkZiY8//hj9+vXDmTNnEBgYWOVtqrJfIqKaJpPJ4ONqDx9X+wpvozcI3CnSQVOsh6bIgMJiPTTFehTeXbT3/vvuumK9AUU6Q8lXvQHFOoEivR7FOmFsu7e+WC9QpLvb7+5Ssk4Y23T6ku30BlHmZWwhgGK9QLFeDxSb82hVzbiuQTUWqJJe8m3evDn69OmDTz/9FEDJv9YaNWqEZ599FnPmzKnyNlXZ7z/xki8R0f0JURKqeoMwhq3OIKAzmAZvsf5um0GU9NEbUGwQ0BtKwlqn/2ubv/cr1hvK3v/d9r/+nL9vZ1rHk+ENMbxToyp/Rqu45JuTk4Pz588jLi7O2CaTydCtWzckJSVVeZuq7JeIiCpPJpOV3INVlFzWruskG6t948YNAIC3t7dJu4+PDzIzM6u8TVX2CwBarRZqtdpkISIiqiiLe/jJYDBUeih4RbZ5UJ+4uDi4ubkZl4CAgErVQEREdZtkgdqgQQMAQFZWlkn7zZs34evrW+VtqrJfAIiNjYVKpTIu6enplfg0RERU10kWqB4eHmjRogUSExONbUIIJCYmokuXLsY2g8EAvV5f4W0qut9/UiqVcHV1NVmIiIgqStJLvm+88QaWL1+OhIQEZGVlYerUqVCr1Zg4caKxz4svvojWrVtXapuK9CEiIjInSZ9DHT16NPLy8vDaa68hMzMT4eHh+Pnnn03uXyoUCtjY2FRqm4r0ISIiMidOPVgOPodKRESVyQKLG+VLRERkjRioREREZiD55PiW6t6VcE7wQERUd93LgIrcHWWgliMvLw8AOJCJiIiQl5cHN7f7T7LPQUnlMBgMuHbtGlxcXKr8El+1Wo2AgACkp6dbxcAma6sXsL6aWW/1s7aaWW/1eth6hRDIy8tDw4YNIZff/y4pz1DLIZfL4e/vb5Z9WdtEEdZWL2B9NbPe6mdtNbPe6vUw9T7ozPQeDkoiIiIyAwYqERGRGTBQq5FSqcQHH3wApVIpdSkVYm31AtZXM+utftZWM+utXjVZLwclERERmQHPUImIiMyAgUpERGQGDFQiIiIz4HOo1eSHH37A6tWrkZeXh6ioKLz55ptwcXGRuiwAQFJSElavXo2UlBT4+flh9OjR6N69u0mfzp07l9pu6tSpGDp0aE2VafTSSy/h2LFjJm2PP/44Zs+ebdJmKcf8mWeeweXLl0u1R0VFYd68eQCAlStXYvHixSbrXVxcsHPnzmqvTwiBn3/+GV999RUyMjKwefNmeHt7l+q3YcMGrFq1CiqVCl26dMG0adNKPcdXkT7mcPr0aSxatAjHjh3DjBkz0Lt3b5P1+fn5+Oqrr7B3714UFxejQ4cOePXVV+Hh4WHsU5PHPDMzE8uWLcNPP/2EPn364L333jNZf+bMGYwZM6bUditXrkRISIjx+1u3biEuLg7JycmoV68eXnzxRTzxxBNmr7ewsBDx8fFYs2YNnJ2dsWHDBpP1iYmJiI2NLXPbpUuXomXLlgCA6OhoaLVak/X/+c9/MHz4cLPWm56ejsWLF+Po0aNwdnZG79698cILL5i86hMAEhISsGLFCqhUKnTu3BlvvfVWqWdKK9KnwgSZ3ZIlS4RSqRSffvqp2Lhxo2jTpo3o2rWrMBgMUpcmVq5cKaKiosSXX34pdu/eLT788ENhY2MjVqxYYdIPgPjss8/EgQMHjMuNGzckqTk6OlqMGjXKpJbz58+b9LGkY37ixAmTWjdt2iQAiPnz5xv7zJw5U4SFhZn0O3LkSI3U98wzz4hevXqJt956SwAQ6enppfosX75c2NnZifnz54uNGzeKtm3bisjISKHX6yvVxxwWLlwoWrZsKf73v/8JAOLrr78u1SciIkJMmTJFbNiwQWzatElERkaKkJAQoVarjX1q6pifOXNG+Pv7i2nTpomIiAjx/PPPl+pz4MABAUDs2bPHpJ78/HxjH41GI0JDQ0V0dLTYvHmzmDVrllAoFCIhIcHsNTdt2lQ899xz4t///rdo3LhxqfXZ2dkmdR44cEAMGTJEeHp6Co1GY+ynVCrFf//7X5N+165dM2utaWlpIjg4WMyePVvs2LFDrFq1Svj7+4thw4aZ9Fu9erWwtbUV8+bNEwkJCaJ9+/aiY8eOQqfTVapPZTBQzUyn0wkfHx/xwQcfGNtSUlIEALFlyxbpCrsrLy+vVNvEiRNFeHi4SRsAsXPnzpoq676io6PFO++8U+56Sz/m//3vf4VSqRS3bt0yts2cOVN06tRJknpu374thBAiMTGxzEDV6/WiQYMGJsf80qVLQiaTiY0bN1a4j7nrFUKUG6j//Lm+efOmkMlkIj4+3thWU8e8oKBAFBUVCSGE6NGjx30Dtay/j/fc+0dibm6usW3MmDGiZcuW5i7ZeIxnzpxZZqD+U1FRkfDx8RGTJ082aVcqlWLz5s1mr+/vtFqt8fjek5CQIACIq1evCiGEMBgMxn/U3JOWliZkMplYv359hftUFu+hmtnp06eRlZWFAQMGGNuCg4MRGhqKXbt2SVhZCWdn5zLbioqKSrVPnz4d3bt3xwsvvIBff/21Jsor14YNGxAdHY1nnnkGq1atMnnzg6Uf8+XLl2PIkCHw8vIyaU9NTUWvXr0wYMAAzJw5E/n5+TVSz4MuZ509exbXr183OZ6BgYEIDw83Hs+K9KmpeoHSP9cODg5QKBSlfq5r4pg7ODjA1ta2Qn1jYmLQs2dPvPLKK7h48aLJut27d6Nr165wd3c3tg0aNAi///47MjMzzVlypS9xbt68GVlZWRg7dmypdbNnz0a3bt0watQoJCYmmqtEIzs7u1LH997//3v/v8+dO4eMjAyTn8+AgABEREQYfz4r0qeyGKhmduXKFQBAw4YNTdobNmxoXGdJbty4geXLl+Opp54yaW/VqhVeeOEFvP3226hXrx569OiBFStWSFKjj48Pnn/+ebz33nuIjIzE66+/jtGjRxvXW/IxP3DgAM6ePYtx48aZtNva2mL48OGYMmUKhg8fjh9++AHt2rXDnTt3JKr0LxU5npZ8zAHg448/hlKpRM+ePY1tlnbMn3zySYwaNQqTJ09GVlYWwsLCcPz4ceP6K1eulHl8762T0rJly9ClSxeEhYWZtIeFhWH06NF455130LBhQ/Tp0weLFi2q1loMBgPi4uLQunVrBAYGApDuZ5iDksysuLgYAErNyuHg4GBcZyny8/MxaNAgBAYG4oMPPjBZd/jwYeNn6NWrF+RyOaZMmYJRo0ZV+e07VfX1118ba+nZsyeaN2+Ovn37YvLkyWjTpo1FH/Nly5YhODgY3bp1M2mfPHmySb29evVCcHAwFi1ahKlTp9ZwlabudzwLCwsr3Ecq69evx4cffojVq1fD19fX2G5JxzwiIgJbtmwxft+/f39069YNsbGx2L59O4CSY1zW8b23TipXr17Fjh07sHTp0lLrkpKSTH5v2NnZ4Y033sC4ceNKDRgyl6lTp+Lw4cPYv3+/se1+P5+5ubkV7lNZPEM1M09PTwBATk6OSXt2dnapS35SunPnDp588klotVrs2LHD+Bf1nn/+kPXs2RO3b99GWlpaTZZZZi2PP/44ZDIZTp48CcByj3l+fj7i4+MxduzYUv8I+ednqlevHtq0aWP8TFKqyPG01GO+adMmPPvss/j8889LjSy1pGNe1jR4PXv2NKnF09OzzOMLQNJjvHLlSjg5OSEmJqbUurJ+b9y5cwepqanVUss777yDpUuXYvv27caRxoB0P8MMVDNr3bo1FAoFjhw5YmzTaDQ4deoUIiIiJKzsLwUFBXjyySdx+/Zt7N69u0I/PDdu3AAAODo6Vnd5D5SVlQUhBJycnABY7jGPj4+HRqPBqFGjKtT/xo0bxs8kpVatWsHGxsbkeBYVFeHkyZPG41mRPjVt8+bNiImJwfz58zFhwoQKbWMpxxwoXUvbtm1x9OhRkz6HDh2Ci4sLmjZtWtPlASh55Gr58uV49tlnK/S74N7vjeo4xu+99x7+97//Yfv27YiMjDRZ17JlS9ja2pr8fBYXF+P48ePGn8+K9Km0Kg1lovsaMmSIaNu2rXEI/KxZs4STk5O4fv26xJWVjEDs3r27aNWqlbh582aZfbZt2yZ+++034/eXLl0SjzzyiOjRo0dNlWmUmpoqVq5caXz8JT8/XwwZMkR4eXmZjP60xGMeGRkphgwZUua6OXPmGEd4GgwGMXfuXONjFDWlvFG+QggRExMj2rRpY6xxzpw5wtHR0TiKsqJ9zA3ljPLdsmWLUCqV4osvvih3WymOeXmjfJctWyYuXrxo/P7XX38Vjo6OJqOmz549KxQKhfGRtqysLBEUFCRefvnlaqv3QaN8d+/eLQCIY8eOlVq3c+dO8csvvxi/T0tLE2FhYSIqKsrsdX7wwQfCxcVF7N+/v9w+w4cPF+Hh4UKlUgkhSkbb29vbi7S0tEr1qQwGajXIysoSUVFRwsXFRQQGBgpPT89qH0peUR999JEAIEJCQkSnTp2My99/6M+dOyd69uwp6tevL0JDQ4WdnZ2IiYkRmZmZNV6vWq0W48ePFx4eHiI8PFy4uLiIDh06iOTkZJN+lnbMz549KwCIbdu2lbl+wYIFwtfXV4SGhgpfX1/RoEEDsWbNmhqpbfHixaJTp06iRYsWAoCIiIgQnTp1Etu3bzf2uXXrlujatatwcXERQUFBwsPDo9TzjxXpYw6HDx82/pwCEE2bNhWdOnUSs2fPNvZxcXERTk5OJj/TnTp1El999ZWxT00e83t/vqurq6hXr57o1KmTeOqpp4zrd+/eLcLCwkRQUJBo2rSpcHBwENOmTRPFxcUm+1m9erVwdnY29unXr5/Js6rmMnHiRNGpUyfh7+8v7OzsjPX/8xnS4cOHi3bt2pW5j9TUVNG3b1/h4+MjwsLChFKpFEOGDDH7c6gnT54UAISvr2+p/9+HDx829svJyRHdunUTzs7OIigoSLi7u4sff/zRZF8V6VMZfNtMNbp48SLy8vIQEhJiMa86unr1KtLT00u1y2QydOrUyaQtOzsb169fR2BgYJmP29SkgoICpKamwtfXt8xZfe6xlGOelZWFixcvomPHjpDLy76zotfrkZKSAkdHR/j7+5fbz9wyMjKQkZFRqj04OBj16tUzabt06RLUavV9j2dF+jwMtVqNs2fPlmr38fFBkyZNAJQMojMYDKX6+Pv7w9/f3/h9TR3zgwcPlmpTKpWlLiWmpaWhsLAQQUFBsLOzK3NfBQUFOHfuHLy8vNCoUaNqqffs2bNQq9Wl2iMiIkz+nx4/fhyenp5o3LhxufvKycnB1atXERgYWC0zld25cwenT58uc11oaGipmbouXboElUqFkJAQ2Nvbl7ldRfpUBAOViIjIDDgoiYiIyAwYqERERGbAQCUiIjIDBioREZEZMFCJiIjMgIFKRERkBgxUIiIiM2CgEtVxaWlp2LBhg9RlEFk9BipRHZeUlFTqfa1EVHl8HypRHZGbm4ujR49CJpOhffv2cHd3R2ZmJg4cOICioiJ89913AEpeEh0eHg6gZJrCY8eOwd3dHW3btjWZgvLSpUs4ffo0+vXrh1OnTiE9PR3t27eHn5+fJJ+PSGoMVKI64Oeff0ZMTAxatWoFJycnnD9/Hp999hkaN26MI0eOQKvVYuPGjQAAuVyO8PBwxMbGYvHixYiMjIRKpcLFixexbt06dO3aFQCwd+9eTJkyBc2bNwcA2NjY4OjRo1i5ciWGDRsm1Uclkk6Vp9UnIqvRrVs38fbbbxu/V6lUYteuXUIIIdauXSu8vLxM+n/77bfC39/f5PV3CxYsEI0bNxY6nU4IIcSKFSsEAPHBBx8Y+8ydO1d4enqavFqPqK7gPVSiOsDBwQEXLlzAnTt3AACurq7o0aNHuf1XrFiB8PBw/Pbbb/j++++xbt062Nvb48qVK7h48aKxn0wmw+uvv278/pVXXkFhYSF27dpVfR+GyELxki9RHTBv3jyMHTsWPj4+iIyMRP/+/TF+/Hg4ODiU2f/y5ctwcHDA+vXrTdqHDRtm8po0Ly8vk1d0KZVKNGzYEFeuXKmeD0JkwRioRHVAixYtsH//fmRlZWHPnj2YOXMm9uzZg02bNpXZ39XVFR07dsTChQvvu1+1Wg2DwWDyXtHc3NxS71Ulqgt4yZeoDrh69SqAkpdyP/PMM5g6darxJdjOzs7QaDQm/fv06YN169YhJyenzP3cU1RUhK1btxq/37t3L27fvo3OnTtXx8cgsmg8QyWqA0aMGAF/f39ERUWhuLgYn376KZ5++mkAQOvWrVFUVIR3330XLVu2RFhYGKZNm4bt27ejQ4cOmDBhAlxdXXHkyBGcOHECR48eNe7X3t4eEydOxJkzZ2BjY4OPPvoI48aNwyOPPCLVRyWSDM9QieqAXbt2oU+fPjh58iTOnTuH2bNn47PPPgMABAQEYMeOHbh9+zYSEhLwxx9/wMXFBfv378d7772HlJQUnDx5Eo8++iiSkpJM9uvl5YVdu3YhPz8fp0+fxocffogvvvhCio9IJDmZEEJIXQQRWZ+VK1fi3XffRUZGhtSlEFkEnqESERGZAQOViKokKCgIgwYNkroMIovBS75ERERmwDNUIiIiM2CgEhERmQEDlYiIyAwYqERERGbAQCUiIjIDBioREZEZMFCJiIjMgIFKRERkBgxUIiIiM/h/vqINU1sRvbQAAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "final loss = 0.0243\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": "29303619", "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, in agreement with the JAX version of this example." ] }, { "cell_type": "code", "execution_count": 12, "id": "9c3ae27a", "metadata": { "execution": { "iopub.execute_input": "2026-09-03T13:34:43.672969Z", "iopub.status.busy": "2026-09-03T13:34:43.672836Z", "iopub.status.idle": "2026-09-03T13:34:45.767839Z", "shell.execute_reply": "2026-09-03T13:34:45.767281Z" } }, "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) = (+0.140, +0.988, -0.000)\n" ] } ], "source": [ "m_T, rho = plot_design(\"final shape and m(T)\")\n", "\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 }