AdjointPlugin4MultiObjective.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "df03ca2b-256f-472c-bcaf-e35a529143c6",
   "metadata": {},
   "source": [
    "# Multi-objective adjoint optimization\n",
    "\n",
    "> Note: Tidy3D now supports automatic differentiation natively through `autograd`. The `jax`-based `adjoint` plugin will be deprecated from 2.7 onwards. To see this notebook implemented in the new feature, see [this notebook](https://www.flexcompute.com/tidy3d/examples/notebooks/Autograd4MultiObjective/).\n",
    "\n",
    "> To install the `jax` module required for this feature, we recommend running `pip install \"tidy3d[jax]\"`.\n",
    "\n",
    "In this notebook, we will show how to use the adjoint plugin efficiently for objectives involving several simulations.\n",
    "\n",
    "One common application of this involves defining an objective function that may depend on several different definitions of your structures, each with some geometric or material modification. For example, including the performance of devices with slightly larger or smaller feature sizes into one's objective can serve to make optimization more robust to fabrication errors. For more details, see this [paper](https://link.springer.com/article/10.1007/s10409-009-0240-z). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "5accbf7e-221b-46b8-8aa4-b010fde0a816",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import jax.numpy as jnp\n",
    "import jax\n",
    "import matplotlib.pylab as plt\n",
    "\n",
    "import tidy3d as td\n",
    "import tidy3d.plugins.adjoint as tda"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a908597-1bb4-45ff-8fc9-dca626011d5c",
   "metadata": {},
   "source": [
    "### Setup\n",
    "\n",
    "First, let's define the frequency that our objective will depend on"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "247c3045-6b11-4a86-9bc7-d9ba1a8c173e",
   "metadata": {},
   "outputs": [],
   "source": [
    "freq0 = 2e14\n",
    "wavelength = td.C_0 / freq0"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d96aca0f-a9da-4f8a-833c-5cefe8a3bb7f",
   "metadata": {},
   "source": [
    "Now we set up some physical parameters.\n",
    "\n",
    "We will be putting a `td.Box` in the center of a domain with a point source on one side and a diffraction monitor on the other.\n",
    "\n",
    "The objective will involve summing the power of the 0th order diffraction order.\n",
    "\n",
    "The gradient of this objective will be computed with respect to the permittivity of the box.\n",
    "\n",
    "We will adjust the size of the box by `dy` in the y direction and define a combined objective function that returns the average power when the box is either perturbed by `+dy`, `0`, or `-dy`, which emulates a treatment for enhancing device robustness via dilation and erosion effects, as described in the paper linked at the top of this notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6894b8a3-4889-431f-bb68-f3bd28b73369",
   "metadata": {},
   "outputs": [],
   "source": [
    "permittivity_val = 2.0\n",
    "\n",
    "# box sizes (original design)\n",
    "lx = wavelength\n",
    "ly = wavelength\n",
    "lz = wavelength\n",
    "\n",
    "# amount by which we will change the box size in y\n",
    "dy = ly / 5.0\n",
    "\n",
    "buffer = 2 * wavelength\n",
    "\n",
    "Lx = lx + 2 * buffer\n",
    "Ly = ly + dy + 2 * buffer\n",
    "Lz = lz + 2 * buffer\n",
    "\n",
    "\n",
    "src_pos_x = -Lx / 2 + buffer / 2\n",
    "mnt_pos_x = +Lx / 2 - buffer / 2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7257c894-0eb8-4813-bc86-8d5ee9b4d639",
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_sim(permittivity: float, dy_sign: int) -> tda.JaxSimulation:\n",
    "    \"\"\"Make a simulation as a function of the box permittivity and the frequency.\"\"\"\n",
    "\n",
    "    box_size = ly + dy_sign * dy\n",
    "    \n",
    "    box = tda.JaxStructure(\n",
    "        geometry=tda.JaxBox(\n",
    "            center=(0.0, 0.0, 0.0),\n",
    "            size=(lx, box_size, lz)\n",
    "        ),\n",
    "        medium=tda.JaxMedium(permittivity=permittivity),\n",
    "    )\n",
    "\n",
    "    src = td.PointDipole(\n",
    "        center=(src_pos_x, 0, 0),\n",
    "        polarization=\"Ey\",\n",
    "        source_time=td.GaussianPulse(\n",
    "            freq0=freq0,\n",
    "            fwidth=freq0/10,\n",
    "        ),\n",
    "    )\n",
    "\n",
    "    mnt = td.DiffractionMonitor(\n",
    "        center=(mnt_pos_x, 0, 0),\n",
    "        size=(0, td.inf, td.inf),\n",
    "        freqs=[freq0],\n",
    "        name=\"diffraction\",\n",
    "    )\n",
    "\n",
    "    return tda.JaxSimulation(\n",
    "        size=(Lx, Ly, Lz),\n",
    "        input_structures=[box],\n",
    "        output_monitors=[mnt],\n",
    "        sources=[src],\n",
    "        grid_spec=td.GridSpec.auto(wavelength=td.C_0 / freq0),\n",
    "        boundary_spec=td.BoundarySpec(\n",
    "            x=td.Boundary.pml(), y=td.Boundary.periodic(), z=td.Boundary.periodic()\n",
    "        ),\n",
    "        run_time=200 / src.source_time.fwidth,\n",
    "    )\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e11b1338-e831-47f6-85d7-d3abe2aef5d5",
   "metadata": {},
   "source": [
    "Let's make a simulation for each of the perturbed size values and visualize them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c03a39c5-83e4-4e0d-84a2-c8bf86446b60",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1000x400 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, axes = plt.subplots(1,3, tight_layout=True, figsize=(10, 4))\n",
    "\n",
    "for ax, dy_sign in zip(axes, (-1, 0, 1)):\n",
    "    jax_sim = make_sim(permittivity=permittivity_val, dy_sign=dy_sign)\n",
    "    ax = jax_sim.plot(z=0, ax=ax)\n",
    "    ax.set_title(f\"size[y]={jax_sim.input_structures[0].geometry.size[1]:.2f}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2aa83e08-2983-4d8d-b85b-31584c96872d",
   "metadata": {},
   "source": [
    "### Define Objective\n",
    "\n",
    "Now let's define our objective function, first we defined how to postprocess a `SimulationData` to give the desired power."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e673c7d6-e44f-4086-bf98-d201739201fc",
   "metadata": {},
   "outputs": [],
   "source": [
    "def post_process(sim_data: tda.JaxSimulationData) -> float:\n",
    "    \"\"\"O-th order diffracted power.\"\"\"\n",
    "    amp = sim_data[\"diffraction\"].amps.sel(orders_x=0, orders_y=0)\n",
    "    return jnp.sum(jnp.abs(amp.values) ** 2)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56d3acce-0f8b-493d-9cf7-0568720827f5",
   "metadata": {},
   "source": [
    "And then we write our combined, multi-objective over all of the `dy` values.  We use the [plugins.adjoint.web.run_async](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.plugins.adjoint.web.run_async.html) function to run a list of these three simulations simultaneously."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "86e4ec1c-89ca-474c-83d1-68c6c3bcbdb3",
   "metadata": {},
   "outputs": [],
   "source": [
    "def objective(permittivity: float) -> float:\n",
    "    \"\"\"Average of O-th order diffracted power over all dy_sign values.\"\"\"\n",
    "    sims = [make_sim(permittivity, dy_sign=dy_sign) for dy_sign in (-1, 0, 1)]\n",
    "    sim_data_list = tda.web.run_async(sims, path_dir=\"data\", verbose=True)\n",
    "    powers = [post_process(sim_data) for sim_data in sim_data_list]\n",
    "    return jnp.mean(jnp.array(powers))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "318b2a19-5536-4332-9903-8f63ce8ae502",
   "metadata": {},
   "source": [
    "### Multi-Objective Gradient Calculation\n",
    "\n",
    "Finally, we are ready to use `jax.value_and_grad` to differentiate this function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "15546df4-05b5-480f-8a10-32a69f434088",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">[10:58:35] </span>Created task <span style=\"color: #008000; text-decoration-color: #008000\">'0_fwd'</span> with task_id                                    \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">           </span><span style=\"color: #008000; text-decoration-color: #008000\">'fdve-b20f9e17-3302-4b67-8159-c83354a27ea1v1'</span>.                       \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m[10:58:35]\u001b[0m\u001b[2;36m \u001b[0mCreated task \u001b[32m'0_fwd'\u001b[0m with task_id                                    \n",
       "\u001b[2;36m           \u001b[0m\u001b[32m'fdve-b20f9e17-3302-4b67-8159-c83354a27ea1v1'\u001b[0m.                       \n"
      ]
     },
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    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">           </span>View task using web UI at                                            \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">           </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-b20f9e17-3302-4b67-8159-c83354a27ea1v1\" target=\"_blank\"><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-b20f9e17-3302-</span></a>\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">           </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-b20f9e17-3302-4b67-8159-c83354a27ea1v1\" target=\"_blank\"><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">4b67-8159-c83354a27ea1v1'</span></a><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">.</span>                                           \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m          \u001b[0m\u001b[2;36m \u001b[0mView task using web UI at                                            \n",
       "\u001b[2;36m           \u001b[0m\u001b]8;id=126246;https://tidy3d.simulation.cloud/workbench?taskId=fdve-b20f9e17-3302-4b67-8159-c83354a27ea1v1\u001b\\\u001b[4;34m'https://tidy3d.simulation.cloud/workbench?\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=347174;https://tidy3d.simulation.cloud/workbench?taskId=fdve-b20f9e17-3302-4b67-8159-c83354a27ea1v1\u001b\\\u001b[4;34mtaskId\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=126246;https://tidy3d.simulation.cloud/workbench?taskId=fdve-b20f9e17-3302-4b67-8159-c83354a27ea1v1\u001b\\\u001b[4;34m=\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=848658;https://tidy3d.simulation.cloud/workbench?taskId=fdve-b20f9e17-3302-4b67-8159-c83354a27ea1v1\u001b\\\u001b[4;34mfdve\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=126246;https://tidy3d.simulation.cloud/workbench?taskId=fdve-b20f9e17-3302-4b67-8159-c83354a27ea1v1\u001b\\\u001b[4;34m-b20f9e17-3302-\u001b[0m\u001b]8;;\u001b\\\n",
       "\u001b[2;36m           \u001b[0m\u001b]8;id=126246;https://tidy3d.simulation.cloud/workbench?taskId=fdve-b20f9e17-3302-4b67-8159-c83354a27ea1v1\u001b\\\u001b[4;34m4b67-8159-c83354a27ea1v1'\u001b[0m\u001b]8;;\u001b\\\u001b[4;34m.\u001b[0m                                           \n"
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       "Output()"
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    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
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     },
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    },
    {
     "data": {
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\n"
      ]
     },
     "metadata": {},
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    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">[10:58:36] </span>Created task <span style=\"color: #008000; text-decoration-color: #008000\">'1_fwd'</span> with task_id                                    \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">           </span><span style=\"color: #008000; text-decoration-color: #008000\">'fdve-aee667ea-d54c-47dd-b1d1-b7652e74ccddv1'</span>.                       \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m[10:58:36]\u001b[0m\u001b[2;36m \u001b[0mCreated task \u001b[32m'1_fwd'\u001b[0m with task_id                                    \n",
       "\u001b[2;36m           \u001b[0m\u001b[32m'fdve-aee667ea-d54c-47dd-b1d1-b7652e74ccddv1'\u001b[0m.                       \n"
      ]
     },
     "metadata": {},
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    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">           </span>View task using web UI at                                            \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">           </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-aee667ea-d54c-47dd-b1d1-b7652e74ccddv1\" target=\"_blank\"><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-aee667ea-d54c-</span></a>\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">           </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-aee667ea-d54c-47dd-b1d1-b7652e74ccddv1\" target=\"_blank\"><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">47dd-b1d1-b7652e74ccddv1'</span></a><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">.</span>                                           \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m          \u001b[0m\u001b[2;36m \u001b[0mView task using web UI at                                            \n",
       "\u001b[2;36m           \u001b[0m\u001b]8;id=803631;https://tidy3d.simulation.cloud/workbench?taskId=fdve-aee667ea-d54c-47dd-b1d1-b7652e74ccddv1\u001b\\\u001b[4;34m'https://tidy3d.simulation.cloud/workbench?\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=821521;https://tidy3d.simulation.cloud/workbench?taskId=fdve-aee667ea-d54c-47dd-b1d1-b7652e74ccddv1\u001b\\\u001b[4;34mtaskId\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=803631;https://tidy3d.simulation.cloud/workbench?taskId=fdve-aee667ea-d54c-47dd-b1d1-b7652e74ccddv1\u001b\\\u001b[4;34m=\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=329856;https://tidy3d.simulation.cloud/workbench?taskId=fdve-aee667ea-d54c-47dd-b1d1-b7652e74ccddv1\u001b\\\u001b[4;34mfdve\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=803631;https://tidy3d.simulation.cloud/workbench?taskId=fdve-aee667ea-d54c-47dd-b1d1-b7652e74ccddv1\u001b\\\u001b[4;34m-aee667ea-d54c-\u001b[0m\u001b]8;;\u001b\\\n",
       "\u001b[2;36m           \u001b[0m\u001b]8;id=803631;https://tidy3d.simulation.cloud/workbench?taskId=fdve-aee667ea-d54c-47dd-b1d1-b7652e74ccddv1\u001b\\\u001b[4;34m47dd-b1d1-b7652e74ccddv1'\u001b[0m\u001b]8;;\u001b\\\u001b[4;34m.\u001b[0m                                           \n"
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       "Output()"
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    {
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      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">[10:58:37] </span>Created task <span style=\"color: #008000; text-decoration-color: #008000\">'2_fwd'</span> with task_id                                    \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">           </span><span style=\"color: #008000; text-decoration-color: #008000\">'fdve-caa12e68-4916-49d0-be89-c04eadb3577ev1'</span>.                       \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m[10:58:37]\u001b[0m\u001b[2;36m \u001b[0mCreated task \u001b[32m'2_fwd'\u001b[0m with task_id                                    \n",
       "\u001b[2;36m           \u001b[0m\u001b[32m'fdve-caa12e68-4916-49d0-be89-c04eadb3577ev1'\u001b[0m.                       \n"
      ]
     },
     "metadata": {},
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    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">           </span>View task using web UI at                                            \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">           </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-caa12e68-4916-49d0-be89-c04eadb3577ev1\" target=\"_blank\"><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-caa12e68-4916-</span></a>\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">           </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-caa12e68-4916-49d0-be89-c04eadb3577ev1\" target=\"_blank\"><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">49d0-be89-c04eadb3577ev1'</span></a><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">.</span>                                           \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m          \u001b[0m\u001b[2;36m \u001b[0mView task using web UI at                                            \n",
       "\u001b[2;36m           \u001b[0m\u001b]8;id=746639;https://tidy3d.simulation.cloud/workbench?taskId=fdve-caa12e68-4916-49d0-be89-c04eadb3577ev1\u001b\\\u001b[4;34m'https://tidy3d.simulation.cloud/workbench?\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=100766;https://tidy3d.simulation.cloud/workbench?taskId=fdve-caa12e68-4916-49d0-be89-c04eadb3577ev1\u001b\\\u001b[4;34mtaskId\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=746639;https://tidy3d.simulation.cloud/workbench?taskId=fdve-caa12e68-4916-49d0-be89-c04eadb3577ev1\u001b\\\u001b[4;34m=\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=508554;https://tidy3d.simulation.cloud/workbench?taskId=fdve-caa12e68-4916-49d0-be89-c04eadb3577ev1\u001b\\\u001b[4;34mfdve\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=746639;https://tidy3d.simulation.cloud/workbench?taskId=fdve-caa12e68-4916-49d0-be89-c04eadb3577ev1\u001b\\\u001b[4;34m-caa12e68-4916-\u001b[0m\u001b]8;;\u001b\\\n",
       "\u001b[2;36m           \u001b[0m\u001b]8;id=746639;https://tidy3d.simulation.cloud/workbench?taskId=fdve-caa12e68-4916-49d0-be89-c04eadb3577ev1\u001b\\\u001b[4;34m49d0-be89-c04eadb3577ev1'\u001b[0m\u001b]8;;\u001b\\\u001b[4;34m.\u001b[0m                                           \n"
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       "Output()"
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    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
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     },
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    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">[10:58:39] </span>Started working on Batch.                                            \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m[10:58:39]\u001b[0m\u001b[2;36m \u001b[0mStarted working on Batch.                                            \n"
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    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">[10:58:40] </span>Maximum FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.075</span> for the whole batch. Use              \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">           </span><span style=\"color: #008000; text-decoration-color: #008000\">'Batch.real_cost()'</span> to get the billed FlexCredit cost after the Batch\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">           </span>has completed.                                                       \n",
       "</pre>\n"
      ],
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       "\u001b[2;36m[10:58:40]\u001b[0m\u001b[2;36m \u001b[0mMaximum FlexCredit cost: \u001b[1;36m0.075\u001b[0m for the whole batch. Use              \n",
       "\u001b[2;36m           \u001b[0m\u001b[32m'Batch.real_cost\u001b[0m\u001b[32m(\u001b[0m\u001b[32m)\u001b[0m\u001b[32m'\u001b[0m to get the billed FlexCredit cost after the Batch\n",
       "\u001b[2;36m           \u001b[0mhas completed.                                                       \n"
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       "Output()"
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    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">[10:58:59] </span>Batch complete.                                                      \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m[10:58:59]\u001b[0m\u001b[2;36m \u001b[0mBatch complete.                                                      \n"
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
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       "</pre>\n"
      ],
      "text/plain": [
       "\n"
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    {
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       "Output()"
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    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\n"
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     },
     "metadata": {},
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    {
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      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">[10:59:01] </span>loading SimulationData from                                          \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">           </span>data/fdve-<span style=\"color: #ffff00; text-decoration-color: #ffff00\">b20f9e17-3302-4b67-8159-c83354a27ea1</span>v1.hdf5                \n",
       "</pre>\n"
      ],
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       "\u001b[2;36m[10:59:01]\u001b[0m\u001b[2;36m \u001b[0mloading SimulationData from                                          \n",
       "\u001b[2;36m           \u001b[0mdata/fdve-\u001b[93mb20f9e17-3302-4b67-8159-c83354a27ea1\u001b[0mv1.hdf5                \n"
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
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     },
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    },
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\n"
      ]
     },
     "metadata": {},
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    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">[10:59:02] </span>loading SimulationData from                                          \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">           </span>data/fdve-<span style=\"color: #ffff00; text-decoration-color: #ffff00\">aee667ea-d54c-47dd-b1d1-b7652e74ccdd</span>v1.hdf5                \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m[10:59:02]\u001b[0m\u001b[2;36m \u001b[0mloading SimulationData from                                          \n",
       "\u001b[2;36m           \u001b[0mdata/fdve-\u001b[93maee667ea-d54c-47dd-b1d1-b7652e74ccdd\u001b[0mv1.hdf5                \n"
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       "Output()"
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    {
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      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
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     },
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">\n",
       "</pre>\n"
      ],
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       "\n"
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     },
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    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">[10:59:03] </span>loading SimulationData from                                          \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">           </span>data/fdve-<span style=\"color: #ffff00; text-decoration-color: #ffff00\">caa12e68-4916-49d0-be89-c04eadb3577e</span>v1.hdf5                \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m[10:59:03]\u001b[0m\u001b[2;36m \u001b[0mloading SimulationData from                                          \n",
       "\u001b[2;36m           \u001b[0mdata/fdve-\u001b[93mcaa12e68-4916-49d0-be89-c04eadb3577e\u001b[0mv1.hdf5                \n"
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      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">[10:59:04] </span>Created task <span style=\"color: #008000; text-decoration-color: #008000\">'0_adj'</span> with task_id                                    \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">           </span><span style=\"color: #008000; text-decoration-color: #008000\">'fdve-c2264f3e-360a-499a-b410-f84ef336d4ecv1'</span>.                       \n",
       "</pre>\n"
      ],
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       "\u001b[2;36m[10:59:04]\u001b[0m\u001b[2;36m \u001b[0mCreated task \u001b[32m'0_adj'\u001b[0m with task_id                                    \n",
       "\u001b[2;36m           \u001b[0m\u001b[32m'fdve-c2264f3e-360a-499a-b410-f84ef336d4ecv1'\u001b[0m.                       \n"
      ]
     },
     "metadata": {},
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    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">           </span>View task using web UI at                                            \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">           </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-c2264f3e-360a-499a-b410-f84ef336d4ecv1\" target=\"_blank\"><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-c2264f3e-360a-</span></a>\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">           </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-c2264f3e-360a-499a-b410-f84ef336d4ecv1\" target=\"_blank\"><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">499a-b410-f84ef336d4ecv1'</span></a><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">.</span>                                           \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m          \u001b[0m\u001b[2;36m \u001b[0mView task using web UI at                                            \n",
       "\u001b[2;36m           \u001b[0m\u001b]8;id=929538;https://tidy3d.simulation.cloud/workbench?taskId=fdve-c2264f3e-360a-499a-b410-f84ef336d4ecv1\u001b\\\u001b[4;34m'https://tidy3d.simulation.cloud/workbench?\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=989345;https://tidy3d.simulation.cloud/workbench?taskId=fdve-c2264f3e-360a-499a-b410-f84ef336d4ecv1\u001b\\\u001b[4;34mtaskId\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=929538;https://tidy3d.simulation.cloud/workbench?taskId=fdve-c2264f3e-360a-499a-b410-f84ef336d4ecv1\u001b\\\u001b[4;34m=\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=677172;https://tidy3d.simulation.cloud/workbench?taskId=fdve-c2264f3e-360a-499a-b410-f84ef336d4ecv1\u001b\\\u001b[4;34mfdve\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=929538;https://tidy3d.simulation.cloud/workbench?taskId=fdve-c2264f3e-360a-499a-b410-f84ef336d4ecv1\u001b\\\u001b[4;34m-c2264f3e-360a-\u001b[0m\u001b]8;;\u001b\\\n",
       "\u001b[2;36m           \u001b[0m\u001b]8;id=929538;https://tidy3d.simulation.cloud/workbench?taskId=fdve-c2264f3e-360a-499a-b410-f84ef336d4ecv1\u001b\\\u001b[4;34m499a-b410-f84ef336d4ecv1'\u001b[0m\u001b]8;;\u001b\\\u001b[4;34m.\u001b[0m                                           \n"
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       "Output()"
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
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     },
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    },
    {
     "data": {
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">\n",
       "</pre>\n"
      ],
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       "\n"
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     },
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    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">[10:59:05] </span>Created task <span style=\"color: #008000; text-decoration-color: #008000\">'1_adj'</span> with task_id                                    \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">           </span><span style=\"color: #008000; text-decoration-color: #008000\">'fdve-0914c5d7-6da1-4127-8b7c-4107cb45dce4v1'</span>.                       \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m[10:59:05]\u001b[0m\u001b[2;36m \u001b[0mCreated task \u001b[32m'1_adj'\u001b[0m with task_id                                    \n",
       "\u001b[2;36m           \u001b[0m\u001b[32m'fdve-0914c5d7-6da1-4127-8b7c-4107cb45dce4v1'\u001b[0m.                       \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">           </span>View task using web UI at                                            \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">           </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-0914c5d7-6da1-4127-8b7c-4107cb45dce4v1\" target=\"_blank\"><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-0914c5d7-6da1-</span></a>\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">           </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-0914c5d7-6da1-4127-8b7c-4107cb45dce4v1\" target=\"_blank\"><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">4127-8b7c-4107cb45dce4v1'</span></a><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">.</span>                                           \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m          \u001b[0m\u001b[2;36m \u001b[0mView task using web UI at                                            \n",
       "\u001b[2;36m           \u001b[0m\u001b]8;id=347652;https://tidy3d.simulation.cloud/workbench?taskId=fdve-0914c5d7-6da1-4127-8b7c-4107cb45dce4v1\u001b\\\u001b[4;34m'https://tidy3d.simulation.cloud/workbench?\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=638906;https://tidy3d.simulation.cloud/workbench?taskId=fdve-0914c5d7-6da1-4127-8b7c-4107cb45dce4v1\u001b\\\u001b[4;34mtaskId\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=347652;https://tidy3d.simulation.cloud/workbench?taskId=fdve-0914c5d7-6da1-4127-8b7c-4107cb45dce4v1\u001b\\\u001b[4;34m=\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=947695;https://tidy3d.simulation.cloud/workbench?taskId=fdve-0914c5d7-6da1-4127-8b7c-4107cb45dce4v1\u001b\\\u001b[4;34mfdve\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=347652;https://tidy3d.simulation.cloud/workbench?taskId=fdve-0914c5d7-6da1-4127-8b7c-4107cb45dce4v1\u001b\\\u001b[4;34m-0914c5d7-6da1-\u001b[0m\u001b]8;;\u001b\\\n",
       "\u001b[2;36m           \u001b[0m\u001b]8;id=347652;https://tidy3d.simulation.cloud/workbench?taskId=fdve-0914c5d7-6da1-4127-8b7c-4107cb45dce4v1\u001b\\\u001b[4;34m4127-8b7c-4107cb45dce4v1'\u001b[0m\u001b]8;;\u001b\\\u001b[4;34m.\u001b[0m                                           \n"
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       "Output()"
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      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
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     },
     "metadata": {},
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    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">\n",
       "</pre>\n"
      ],
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       "\n"
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     },
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    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">           </span>Created task <span style=\"color: #008000; text-decoration-color: #008000\">'2_adj'</span> with task_id                                    \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">           </span><span style=\"color: #008000; text-decoration-color: #008000\">'fdve-1ac8f06a-d66a-43de-b7a3-035bb6ca86b9v1'</span>.                       \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m          \u001b[0m\u001b[2;36m \u001b[0mCreated task \u001b[32m'2_adj'\u001b[0m with task_id                                    \n",
       "\u001b[2;36m           \u001b[0m\u001b[32m'fdve-1ac8f06a-d66a-43de-b7a3-035bb6ca86b9v1'\u001b[0m.                       \n"
      ]
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    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">           </span>View task using web UI at                                            \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">           </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-1ac8f06a-d66a-43de-b7a3-035bb6ca86b9v1\" target=\"_blank\"><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-1ac8f06a-d66a-</span></a>\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">           </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-1ac8f06a-d66a-43de-b7a3-035bb6ca86b9v1\" target=\"_blank\"><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">43de-b7a3-035bb6ca86b9v1'</span></a><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">.</span>                                           \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m          \u001b[0m\u001b[2;36m \u001b[0mView task using web UI at                                            \n",
       "\u001b[2;36m           \u001b[0m\u001b]8;id=252486;https://tidy3d.simulation.cloud/workbench?taskId=fdve-1ac8f06a-d66a-43de-b7a3-035bb6ca86b9v1\u001b\\\u001b[4;34m'https://tidy3d.simulation.cloud/workbench?\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=389906;https://tidy3d.simulation.cloud/workbench?taskId=fdve-1ac8f06a-d66a-43de-b7a3-035bb6ca86b9v1\u001b\\\u001b[4;34mtaskId\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=252486;https://tidy3d.simulation.cloud/workbench?taskId=fdve-1ac8f06a-d66a-43de-b7a3-035bb6ca86b9v1\u001b\\\u001b[4;34m=\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=456204;https://tidy3d.simulation.cloud/workbench?taskId=fdve-1ac8f06a-d66a-43de-b7a3-035bb6ca86b9v1\u001b\\\u001b[4;34mfdve\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=252486;https://tidy3d.simulation.cloud/workbench?taskId=fdve-1ac8f06a-d66a-43de-b7a3-035bb6ca86b9v1\u001b\\\u001b[4;34m-1ac8f06a-d66a-\u001b[0m\u001b]8;;\u001b\\\n",
       "\u001b[2;36m           \u001b[0m\u001b]8;id=252486;https://tidy3d.simulation.cloud/workbench?taskId=fdve-1ac8f06a-d66a-43de-b7a3-035bb6ca86b9v1\u001b\\\u001b[4;34m43de-b7a3-035bb6ca86b9v1'\u001b[0m\u001b]8;;\u001b\\\u001b[4;34m.\u001b[0m                                           \n"
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       "Output()"
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    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
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     },
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    {
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\n"
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    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">[10:59:07] </span>Started working on Batch.                                            \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m[10:59:07]\u001b[0m\u001b[2;36m \u001b[0mStarted working on Batch.                                            \n"
      ]
     },
     "metadata": {},
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    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">[10:59:09] </span>Maximum FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.075</span> for the whole batch. Use              \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">           </span><span style=\"color: #008000; text-decoration-color: #008000\">'Batch.real_cost()'</span> to get the billed FlexCredit cost after the Batch\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">           </span>has completed.                                                       \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m[10:59:09]\u001b[0m\u001b[2;36m \u001b[0mMaximum FlexCredit cost: \u001b[1;36m0.075\u001b[0m for the whole batch. Use              \n",
       "\u001b[2;36m           \u001b[0m\u001b[32m'Batch.real_cost\u001b[0m\u001b[32m(\u001b[0m\u001b[32m)\u001b[0m\u001b[32m'\u001b[0m to get the billed FlexCredit cost after the Batch\n",
       "\u001b[2;36m           \u001b[0mhas completed.                                                       \n"
      ]
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      "average power = 2.62e+00\n",
      "derivative of average power wrt permittivity = -8.79e-01\n"
     ]
    }
   ],
   "source": [
    "grad_objective = jax.value_and_grad(objective)\n",
    "\n",
    "power_average, grad_power_min = grad_objective(permittivity_val)\n",
    "print(f\"average power = {power_average:.2e}\")\n",
    "print(f\"derivative of average power wrt permittivity = {grad_power_min:.2e}\")\n"
   ]
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    "### Sanity Checking: Manual Loop over size\n",
    "\n",
    "Now we will implement the brute force approach to computing the multi-objective gradient by the naive approach of looping over dy values and computing the individual gradient contributions one by one."
   ]
  },
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   "cell_type": "code",
   "execution_count": 9,
   "id": "722f8199-6316-49d0-a53d-2e39c3f649cd",
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    "def grad_manual(permittivity: float) -> float:\n",
    "    \"\"\"Average of O-th order diffracted power over all dy_sign values.\"\"\"\n",
    "\n",
    "    grad_avg = 0.0\n",
    "\n",
    "    for dy_sign in (-1, 0, 1):\n",
    "        print(f\"working on dy_sign = {dy_sign}\")\n",
    "\n",
    "        def objective_fn(p):\n",
    "            sims = make_sim(p, dy_sign=dy_sign)\n",
    "            sim_data = tda.web.run(sims, task_name=f\"dy_sign={dy_sign}\", verbose=False)\n",
    "            return post_process(sim_data)\n",
    "    \n",
    "        grad_fn = jax.grad(objective_fn)\n",
    "        \n",
    "        gradient = grad_fn(permittivity)\n",
    "        grad_avg += gradient / 3.0\n",
    "        \n",
    "    return grad_avg\n"
   ]
  },
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   "cell_type": "code",
   "execution_count": 10,
   "id": "4662f3ea-ec95-4d40-8ac9-255ca3228b18",
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "working on dy_sign = -1\n",
      "working on dy_sign = 0\n",
      "working on dy_sign = 1\n"
     ]
    }
   ],
   "source": [
    "grad_man = grad_manual(permittivity_val)\n"
   ]
  },
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   "cell_type": "markdown",
   "id": "274b87fc-b3d4-4d33-a782-d0338b694220",
   "metadata": {},
   "source": [
    "We can see that they match, as expected."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "24aa18da-fa10-4307-acde-ca0ac24bf98e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gradient (batched) = -8.7947e-01\n",
      "gradient (looped) = -8.7947e-01\n"
     ]
    }
   ],
   "source": [
    "print(f\"gradient (batched) = {grad_power_min:.4e}\")\n",
    "print(f\"gradient (looped) = {grad_man:.4e}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2386142b-fe8e-4fa2-b80d-942db85b4d0c",
   "metadata": {},
   "source": [
    "## Takeaways\n",
    "\n",
    "The main thing to note here is that, using [plugins.adjoint.web.run_async](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.plugins.adjoint.web.run_async.html), all of the individual simulations were uploaded at roughly the same time.\n",
    "\n",
    "This means that the server is able to work on them concurrently rather than needing to wait for the previously uploaded one to finish. The time savings for applications with several simulations can be enormous.\n",
    "\n",
    "> Note: Native support for multi-frequency output monitors was added in Tidy3D 2.5. Previously it was recommended that users use the `run_async` approach described here for multi-frequency objectives, but this is no longer necessary. That being said, for objectives with very tightly-packed frequency spacing in the output monitors, using a batch approach such as described here may be advantageous as the multi-frequency adjoint approach requires a run_time that scales inversely with the difference between frequency points, potentially requiring long simulation run times. The overall wait time may therefore be shorter using a batch approach."
   ]
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  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8595d30c-cba4-4a08-9967-e6ecef80d98f",
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  {
   "cell_type": "code",
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  "description": "This notebook demonstrates how to perform multi-objective adjoint optimization in Tidy3D FDTD using the adjoint plugin.",
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