{ "cells": [ { "cell_type": "markdown", "id": "fed083e4-9be1-480c-82e9-4bfd7dbccf1f", "metadata": {}, "source": [ "# Adjoint Plugin: 2 Checking Gradients\n", "\n", "In this notebook, we will show how to use the adjoint plugin for `DiffractionMonitor` outputs and also check the gradient values against gradients obtained using transfer matrix method (TMM) to validate their accuracy for a multilayer slab problem." ] }, { "cell_type": "code", "execution_count": 1, "id": "51963da1", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
[14:48:02] INFO     Using client version: 1.9.0rc1                                                  __init__.py:121\n",
       "
\n" ], "text/plain": [ "\u001b[2;36m[14:48:02]\u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO \u001b[0m Using client version: \u001b[1;36m1.9\u001b[0m.0rc1 \u001b]8;id=396746;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/__init__.py\u001b\\\u001b[2m__init__.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=281179;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/__init__.py#121\u001b\\\u001b[2m121\u001b[0m\u001b]8;;\u001b\\\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import jax.numpy as jnp\n", "import jax\n", "import tmm\n", "import matplotlib.pyplot as plt\n", "from typing import Tuple, List\n", "\n", "import tidy3d as td\n", "from tidy3d.web import run as run_sim\n", "from tidy3d.plugins.adjoint import JaxSimulation, JaxBox, JaxMedium, JaxStructure, JaxSimulationData\n", "from tidy3d.plugins.adjoint.web import run as run_adjoint" ] }, { "cell_type": "markdown", "id": "b33d0892-62d3-4329-810f-f29ce10056b4", "metadata": {}, "source": [ "First, we define some global parameters describing the transmission through a multilayer slab with some spacing between each slab.\n", "\n", "The layout is diagrammed below.\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 2, "id": "ccbd2c6a-419d-4570-8f91-f57ad5bad813", "metadata": {}, "outputs": [], "source": [ "# frequency we want to simulate at\n", "freq0 = 2.0e14\n", "k0 = 2 * np.pi * freq0 / td.C_0\n", "freqs = [freq0]\n", "wavelength = td.C_0 / freq0\n", "\n", "# background permittivity\n", "bck_eps = 1.3**2\n", "\n", "# space between each slab\n", "spc = 0.1\n", "\n", "# slab permittivities and thicknesses\n", "slab_eps0 = [2.**2, 1.8**2, 1.5**2, 1.9**2]\n", "slab_ds0 = [0.5, 0.25, 0.5, 0.5]\n", "\n", "# incidence angle\n", "theta = np.pi/8\n", "\n", "# resolution\n", "dl = 0.01" ] }, { "cell_type": "markdown", "id": "48dd37b0-ba97-45cd-a861-53ea6ae3fa74", "metadata": {}, "source": [ "## Transfer Matrix Method (Ground Truth)\n", "\n", "Next we use the `tmm` package to write a function to return the transmission `T` of `p` polarized light given a set of slab permittivities and thicknesses. We'll also write a function to compute the numerical gradient using TMM and will take these to be our \"ground truths\" when evaluating the accuracy of our values obtained through FDTD and the adjoint plugin.\n", "\n", "### Transmission Calculation with TMM\n", "\n", "First, we write a function to compute transmission." ] }, { "cell_type": "code", "execution_count": 3, "id": "cc4f6e91-6a53-476e-b4c6-e76e50246426", "metadata": {}, "outputs": [], "source": [ "def compute_T_tmm(slab_eps=slab_eps0, slab_ds=slab_ds0) -> float:\n", " \"\"\"Get transmission as a function of slab permittivities and thicknesses.\"\"\"\n", "\n", " # construct lists of permittivities and thicknesses including spaces between\n", " new_slab_eps = []\n", " new_slab_ds = []\n", " for eps, d in zip(slab_eps, slab_ds):\n", " new_slab_eps.append(eps)\n", " new_slab_eps.append(bck_eps)\n", " new_slab_ds.append(d)\n", " new_slab_ds.append(spc)\n", " slab_eps = new_slab_eps[:-1]\n", " slab_ds = new_slab_ds[:-1]\n", "\n", " # add the input and output spaces to the lists\n", " eps_list = [bck_eps] + slab_eps + [bck_eps]\n", " n_list = np.sqrt(eps_list) \n", " d_list = [np.inf] + slab_ds + [np.inf]\n", " \n", " # compute transmission with TMM\n", " return tmm.coh_tmm(\"p\", n_list, d_list, theta, wavelength)[\"T\"]" ] }, { "cell_type": "markdown", "id": "c6c0da6b-2d2f-4be5-80e6-c84afd8d1a23", "metadata": {}, "source": [ "We run this function with our starting parameters and see that we get a transmission of about 98% for the set of input parameters." ] }, { "cell_type": "code", "execution_count": 4, "id": "c1743e54-d7f3-468a-8ac4-d42d4c2bc8dc", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "T (tmm) = 0.997\n" ] } ], "source": [ "T_tmm = compute_T_tmm(slab_eps=slab_eps0, slab_ds=slab_ds0)\n", "print(f\"T (tmm) = {T_tmm:.3f}\")" ] }, { "cell_type": "markdown", "id": "452db467-f486-468d-8ec9-b9e669755c92", "metadata": {}, "source": [ "### Numerical Gradient with TMM\n", "\n", "Next, we will use our `compute_T_tmm()` function to compute the \"numerical\" gradient to use as comparison against our adjoint results with FDTD.\n", "\n", "The derivative of a function $f(x)$ w.r.t. $x$ can be approximated using finite differences as\n", "\n", "$$ \\frac{df}{dx}(x) \\approx \\frac{f(x+\\Delta) - f(x-\\Delta)}{2\\Delta}$$\n", "\n", "with a small step $\\Delta$.\n", "\n", "To compute the gradient of our transmission with respect to each of the slab thicknesses and permittivities, we need to repeat this step for each of the values. Luckily, since TMM is very fast, we can compute these quantities quite quickly compared to if we were using FDTD.\n", "\n", "Here we write a function to return this gradient." ] }, { "cell_type": "code", "execution_count": 5, "id": "15d5bae1-6fc7-41c8-8772-2e80505be17d", "metadata": {}, "outputs": [], "source": [ "def compute_grad_tmm(slab_eps=slab_eps0, slab_ds=slab_ds0) -> Tuple[List[float], List[float]]:\n", " \"\"\"Compute numerical gradient of transmission w.r.t. each of the slab permittivities and thicknesses using TMM.\"\"\"\n", "\n", " delta = 1e-4\n", "\n", " # set up containers to store gradient and perturbed arguments\n", " num_slabs = len(slab_eps)\n", " grad_tmm = np.zeros((2, num_slabs), dtype=float)\n", " args = np.stack((slab_eps, slab_ds), axis=0)\n", "\n", " # loop through slab index and argument index (eps, d)\n", " for arg_index in range(2):\n", " for slab_index in range(num_slabs):\n", " grad = 0.0\n", " \n", " # perturb the argument by delta in each + and - direction\n", " for pm in (-1, +1):\n", " args_num = args.copy()\n", " args_num[arg_index][slab_index] += delta * pm\n", " \n", " # compute argument perturbed T and add to finite difference gradient contribution\n", " T_tmm = compute_T_tmm(slab_eps=args_num[0], slab_ds=args_num[1])\n", " grad += pm * T_tmm / 2 / delta \n", "\n", " grad_tmm[arg_index][slab_index] = grad\n", " grad_eps, grad_ds = grad_tmm\n", " return grad_eps, grad_ds" ] }, { "cell_type": "markdown", "id": "d3c362ca-fb31-4ead-8e7c-fcc24d0faecc", "metadata": {}, "source": [ "Let's run this function and observe the gradients. These will be saved later to compare against our adjoint plugin results." ] }, { "cell_type": "code", "execution_count": 6, "id": "b5d1cc93-6d6e-43a7-8e5f-f1829770f3d5", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "gradient w.r.t. eps (tmm) = [ 0.00353246 0.0255666 0.02079163 -0.00767556]\n", "gradient w.r.t. ds (tmm) = [ 0.12389213 0.27248157 0.14586663 -0.02167071]\n" ] } ], "source": [ "grad_eps_tmm, grad_ds_tmm = compute_grad_tmm()\n", "print(f\"gradient w.r.t. eps (tmm) = {grad_eps_tmm}\")\n", "print(f\"gradient w.r.t. ds (tmm) = {grad_ds_tmm}\")" ] }, { "cell_type": "markdown", "id": "50ca68ae-ca5a-49aa-9969-ac6d43324ea9", "metadata": {}, "source": [ "## FDTD (Using adjoint plugin)\n", "\n", "Next, we will implement the same two functions using Tidy3D's adjoint plugin.\n", "\n", "### Transmission Calculation with FDTD\n", "\n", "We first write a function to compute the transmission of a multilayer slab using Tidy3D.\n", "\n", "As discussed in the previous adjoint tutorial notebook, we need to use `jax`-compatible components from the tidy3d subclass for any structures that may depend on the parameters. In this case, this means that the slabs must be `JaxStructures` containing `JaxBox` and `JaxMedium` and must be added to `JaxSimulation.input_structures`.\n", "\n", "We use a `DiffractionMonitor` to measure our transmission amplitudes. As the data corresponding to this monitor will be used in the differentiable function return value, we must add it to `JaxSimulation.output_monitors`.\n", "\n", "Below, we break up the transmission calculation into a few functions to make it easier to read and re-use later." ] }, { "cell_type": "code", "execution_count": 7, "id": "4d12f133-a8d8-4e59-938f-fca4d2e2fa0b", "metadata": {}, "outputs": [], "source": [ "def make_sim(slab_eps=slab_eps0, slab_ds=slab_ds0) -> JaxSimulation:\n", " \"\"\"Create a JaxSimulation given the slab permittivities and thicknesses.\"\"\"\n", "\n", " # frequency setup\n", " wavelength = td.C_0 / freq0\n", " fwidth = freq0 / 10.0\n", " freqs = [freq0]\n", "\n", " # geometry setup\n", " bck_medium = td.Medium(permittivity=bck_eps)\n", "\n", " space_above = 2\n", " space_below = 2\n", "\n", " length_x = 0.1\n", " length_y = 0.1\n", " length_z = space_below + sum(slab_ds0) + space_above + (len(slab_ds0) - 1) * spc\n", " sim_size = (length_x, length_y, length_z)\n", "\n", " # make structures\n", " slabs = []\n", " z_start = -length_z/2 + space_below\n", " for (d, eps) in zip(slab_ds, slab_eps):\n", " slab = JaxStructure(\n", " geometry=JaxBox(center=[0, 0, z_start + d / 2], size=[td.inf, td.inf, d]),\n", " medium=JaxMedium(permittivity=eps),\n", " )\n", " slabs.append(slab)\n", " z_start += d + spc\n", "\n", " # source setup\n", " gaussian = td.GaussianPulse(freq0=freq0, fwidth=fwidth)\n", " src_z = -length_z/2 + space_below/2.0\n", "\n", " source = td.PlaneWave(\n", " center=(0, 0, src_z),\n", " size=(td.inf, td.inf, 0),\n", " source_time=gaussian,\n", " direction=\"+\",\n", " angle_theta=theta,\n", " angle_phi=0,\n", " pol_angle=0,\n", " )\n", "\n", " # boundaries\n", " boundary_x = td.Boundary.bloch_from_source(\n", " source=source, domain_size=sim_size[0], axis=0, medium=bck_medium\n", " )\n", " boundary_y = td.Boundary.bloch_from_source(\n", " source=source, domain_size=sim_size[1], axis=1, medium=bck_medium\n", " ) \n", " boundary_spec = td.BoundarySpec(x=boundary_x, y=boundary_y, z=td.Boundary.pml(num_layers=40))\n", "\n", " # monitors\n", " mnt_z = length_z/2 - space_above/2.0\n", " monitor_1 = td.DiffractionMonitor(\n", " center=[0.0, 0.0, mnt_z],\n", " size=[td.inf, td.inf, 0],\n", " freqs=freqs,\n", " name=\"diffraction\",\n", " normal_dir=\"+\",\n", " )\n", "\n", " # make simulation\n", " return JaxSimulation(\n", " size=sim_size,\n", " grid_spec=td.GridSpec.auto(min_steps_per_wvl=100),\n", " input_structures=slabs,\n", " sources=[source],\n", " output_monitors=[monitor_1],\n", " run_time= 10 / fwidth,\n", " boundary_spec=boundary_spec,\n", " medium=bck_medium,\n", " subpixel=True,\n", " shutoff=1e-8,\n", " )" ] }, { "cell_type": "markdown", "id": "9addea1f-4dd8-4e5e-a058-b94638fb2d70", "metadata": {}, "source": [ "Let's generate a simulation and plot it to make sure it looks reasonable." ] }, { "cell_type": "code", "execution_count": 8, "id": "bc0dc456-e742-4299-ae5e-22daa49e3997", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
           INFO     Auto meshing using wavelength 1.4990 defined from sources.                     grid_spec.py:510\n",
       "
\n" ], "text/plain": [ "\u001b[2;36m \u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO \u001b[0m Auto meshing using wavelength \u001b[1;36m1.4990\u001b[0m defined from sources. \u001b]8;id=324563;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/components/grid/grid_spec.py\u001b\\\u001b[2mgrid_spec.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=646067;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/components/grid/grid_spec.py#510\u001b\\\u001b[2m510\u001b[0m\u001b]8;;\u001b\\\n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sim = make_sim()\n", "f, ax = plt.subplots(1, 1, figsize=(10, 10))\n", "sim.plot(y=0, ax=ax)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "e4c9a742-5988-444d-9ac4-34b612d42289", "metadata": {}, "source": [ "Now we write a function to post process some run results to get the transmission we are after." ] }, { "cell_type": "code", "execution_count": 9, "id": "1917a8b6-8ba9-4767-90ca-06cd6daadcd3", "metadata": {}, "outputs": [], "source": [ "def post_process_T(sim_data: JaxSimulationData) -> float:\n", " \"\"\"Given some JaxSimulationData from the run, return the transmission of \"p\" polarized light.\"\"\"\n", " amps = sim_data.output_monitor_data[\"diffraction\"].amps.sel(polarization=\"p\")\n", " return jnp.sum(abs(amps.values)**2)" ] }, { "cell_type": "markdown", "id": "b65e4d49-e8b1-4e05-9fce-57bd63b3f2cf", "metadata": {}, "source": [ "And finally, put everything together in a single function that relates the permittivities and thicknesses of each slab to the transmission, through a `JaxSimulation` run using the adjoint plugin." ] }, { "cell_type": "code", "execution_count": 10, "id": "f64ac290-b67d-4a9a-88e8-504de931fef8", "metadata": {}, "outputs": [], "source": [ "def compute_T_fdtd(slab_eps=slab_eps0, slab_ds=slab_ds0) -> float:\n", " \"\"\"Given the slab permittivities and thicknesses, compute T, making sure to use `tidy3d.plugins.adjoint.web.run_adjoint`.\"\"\"\n", " sim = make_sim(slab_eps=slab_eps, slab_ds=slab_ds)\n", " sim_data = run_adjoint(sim, task_name='slab')\n", " return post_process_T(sim_data)" ] }, { "cell_type": "markdown", "id": "c4c19d59-d9a3-4935-b785-5fb6b3b3a819", "metadata": {}, "source": [ "### Computing T and Gradient with FDTD\n", "\n", "Now that we have this function defined, we are ready to compute our transmission and gradients using Tidy3d.\n", "\n", "We first call `jax.value_and_grad()` on our transmission calculation function, which returns a function that will give us both `T` and the gradient of `T` with respect to the input parameters in one shot. For more details, see the previous tutorial." ] }, { "cell_type": "code", "execution_count": 11, "id": "59647cdf-8c2a-40d6-bbc9-b7537616938a", "metadata": {}, "outputs": [], "source": [ "compute_T_and_grad_fdtd = jax.value_and_grad(compute_T_fdtd, argnums=(0, 1))" ] }, { "cell_type": "markdown", "id": "81caed90-8554-441b-8948-b240e181e98c", "metadata": {}, "source": [ "Next, we call this function on our starting parameters, which will kick off the original (`fwd`) T transmission simulation and then the reverse (`adj`) simulation, which is used in combination with `fwd` for the gradient calculation." ] }, { "cell_type": "code", "execution_count": 12, "id": "ef6716b3-79a3-40cc-ac2a-5056b5ed2ae9", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
[14:48:03] INFO     Remote TPU is not linked into jax; skipping remote TPU.                       xla_bridge.py:160\n",
       "
\n" ], "text/plain": [ "\u001b[2;36m[14:48:03]\u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO \u001b[0m Remote TPU is not linked into jax; skipping remote TPU. \u001b]8;id=989308;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/jax/_src/lib/xla_bridge.py\u001b\\\u001b[2mxla_bridge.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=231243;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/jax/_src/lib/xla_bridge.py#160\u001b\\\u001b[2m160\u001b[0m\u001b]8;;\u001b\\\n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "
           INFO     Unable to initialize backend 'tpu_driver': Could not initialize backend       xla_bridge.py:333\n",
       "                    'tpu_driver'                                                                                   \n",
       "
\n" ], "text/plain": [ "\u001b[2;36m \u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO \u001b[0m Unable to initialize backend \u001b[32m'tpu_driver'\u001b[0m: Could not initialize backend \u001b]8;id=289490;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/jax/_src/lib/xla_bridge.py\u001b\\\u001b[2mxla_bridge.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=323676;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/jax/_src/lib/xla_bridge.py#333\u001b\\\u001b[2m333\u001b[0m\u001b]8;;\u001b\\\n", "\u001b[2;36m \u001b[0m \u001b[32m'tpu_driver'\u001b[0m \u001b[2m \u001b[0m\n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "
           INFO     Unable to initialize backend 'cuda': module 'jaxlib.xla_extension' has no     xla_bridge.py:333\n",
       "                    attribute 'GpuAllocatorConfig'                                                                 \n",
       "
\n" ], "text/plain": [ "\u001b[2;36m \u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO \u001b[0m Unable to initialize backend \u001b[32m'cuda'\u001b[0m: module \u001b[32m'jaxlib.xla_extension'\u001b[0m has no \u001b]8;id=998228;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/jax/_src/lib/xla_bridge.py\u001b\\\u001b[2mxla_bridge.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=773790;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/jax/_src/lib/xla_bridge.py#333\u001b\\\u001b[2m333\u001b[0m\u001b]8;;\u001b\\\n", "\u001b[2;36m \u001b[0m attribute \u001b[32m'GpuAllocatorConfig'\u001b[0m \u001b[2m \u001b[0m\n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "
           INFO     Unable to initialize backend 'rocm': module 'jaxlib.xla_extension' has no     xla_bridge.py:333\n",
       "                    attribute 'GpuAllocatorConfig'                                                                 \n",
       "
\n" ], "text/plain": [ "\u001b[2;36m \u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO \u001b[0m Unable to initialize backend \u001b[32m'rocm'\u001b[0m: module \u001b[32m'jaxlib.xla_extension'\u001b[0m has no \u001b]8;id=552431;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/jax/_src/lib/xla_bridge.py\u001b\\\u001b[2mxla_bridge.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=398896;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/jax/_src/lib/xla_bridge.py#333\u001b\\\u001b[2m333\u001b[0m\u001b]8;;\u001b\\\n", "\u001b[2;36m \u001b[0m attribute \u001b[32m'GpuAllocatorConfig'\u001b[0m \u001b[2m \u001b[0m\n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "
           INFO     Unable to initialize backend 'tpu': module 'jaxlib.xla_extension' has no      xla_bridge.py:333\n",
       "                    attribute 'get_tpu_client'                                                                     \n",
       "
\n" ], "text/plain": [ "\u001b[2;36m \u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO \u001b[0m Unable to initialize backend \u001b[32m'tpu'\u001b[0m: module \u001b[32m'jaxlib.xla_extension'\u001b[0m has no \u001b]8;id=895050;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/jax/_src/lib/xla_bridge.py\u001b\\\u001b[2mxla_bridge.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=248335;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/jax/_src/lib/xla_bridge.py#333\u001b\\\u001b[2m333\u001b[0m\u001b]8;;\u001b\\\n", "\u001b[2;36m \u001b[0m attribute \u001b[32m'get_tpu_client'\u001b[0m \u001b[2m \u001b[0m\n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "
           INFO     Auto meshing using wavelength 1.4990 defined from sources.                     grid_spec.py:510\n",
       "
\n" ], "text/plain": [ "\u001b[2;36m \u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO \u001b[0m Auto meshing using wavelength \u001b[1;36m1.4990\u001b[0m defined from sources. \u001b]8;id=973489;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/components/grid/grid_spec.py\u001b\\\u001b[2mgrid_spec.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=340501;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/components/grid/grid_spec.py#510\u001b\\\u001b[2m510\u001b[0m\u001b]8;;\u001b\\\n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "
[14:48:04] INFO     Created task 'slab_fwd' with task_id 'b009d1ea-09fb-4fab-bb67-8b46aeb63e18'.      webapi.py:120\n",
       "
\n" ], "text/plain": [ "\u001b[2;36m[14:48:04]\u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO \u001b[0m Created task \u001b[32m'slab_fwd'\u001b[0m with task_id \u001b[32m'b009d1ea-09fb-4fab-bb67-8b46aeb63e18'\u001b[0m. \u001b]8;id=307600;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py\u001b\\\u001b[2mwebapi.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=291689;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py#120\u001b\\\u001b[2m120\u001b[0m\u001b]8;;\u001b\\\n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "
\n"
      ],
      "text/plain": [
       "\u001b[?25l"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "463ceb3a867247e9a45250eb8f56650f",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
\n",
       "
\n"
      ],
      "text/plain": [
       "\n",
       "\u001b[?25h"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
[14:48:06] INFO     Maximum FlexUnit cost: 0.025                                                      webapi.py:253\n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m[14:48:06]\u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO    \u001b[0m Maximum FlexUnit cost: \u001b[1;36m0.025\u001b[0m                                                      \u001b]8;id=60131;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py\u001b\\\u001b[2mwebapi.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=664184;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py#253\u001b\\\u001b[2m253\u001b[0m\u001b]8;;\u001b\\\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
           INFO     status = queued                                                                   webapi.py:262\n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m          \u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO    \u001b[0m status = queued                                                                   \u001b]8;id=316574;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py\u001b\\\u001b[2mwebapi.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=938653;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py#262\u001b\\\u001b[2m262\u001b[0m\u001b]8;;\u001b\\\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
\n"
      ],
      "text/plain": [
       "\u001b[?25l"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
[14:48:09] INFO     status = preprocess                                                               webapi.py:274\n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m[14:48:09]\u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO    \u001b[0m status = preprocess                                                               \u001b]8;id=692349;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py\u001b\\\u001b[2mwebapi.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=709185;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py#274\u001b\\\u001b[2m274\u001b[0m\u001b]8;;\u001b\\\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
\n",
       "
\n"
      ],
      "text/plain": [
       "\n",
       "\u001b[?25h\r",
       "\u001b[1A\u001b[2K"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
[14:48:13] INFO     starting up solver                                                                webapi.py:278\n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m[14:48:13]\u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO    \u001b[0m starting up solver                                                                \u001b]8;id=192222;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py\u001b\\\u001b[2mwebapi.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=523591;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py#278\u001b\\\u001b[2m278\u001b[0m\u001b]8;;\u001b\\\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
[14:48:20] INFO     running solver                                                                    webapi.py:284\n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m[14:48:20]\u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO    \u001b[0m running solver                                                                    \u001b]8;id=677288;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py\u001b\\\u001b[2mwebapi.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=9756;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py#284\u001b\\\u001b[2m284\u001b[0m\u001b]8;;\u001b\\\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
\n"
      ],
      "text/plain": [
       "\u001b[?25l"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d83c27b9143542fa86b3d0d4c1ea22a3",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
[14:48:22] INFO     early shutoff detected, exiting.                                                  webapi.py:295\n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m[14:48:22]\u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO    \u001b[0m early shutoff detected, exiting.                                                  \u001b]8;id=927438;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py\u001b\\\u001b[2mwebapi.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=709260;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py#295\u001b\\\u001b[2m295\u001b[0m\u001b]8;;\u001b\\\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
\n",
       "
\n"
      ],
      "text/plain": [
       "\n",
       "\u001b[?25h"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
           INFO     status = postprocess                                                              webapi.py:301\n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m          \u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO    \u001b[0m status = postprocess                                                              \u001b]8;id=5435;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py\u001b\\\u001b[2mwebapi.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=547529;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py#301\u001b\\\u001b[2m301\u001b[0m\u001b]8;;\u001b\\\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
\n"
      ],
      "text/plain": [
       "\u001b[?25l"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
[14:48:26] INFO     status = success                                                                  webapi.py:307\n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m[14:48:26]\u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO    \u001b[0m status = success                                                                  \u001b]8;id=489495;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py\u001b\\\u001b[2mwebapi.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=217568;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py#307\u001b\\\u001b[2m307\u001b[0m\u001b]8;;\u001b\\\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
\n",
       "
\n"
      ],
      "text/plain": [
       "\n",
       "\u001b[?25h\r",
       "\u001b[1A\u001b[2K"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
           INFO     Billed FlexUnit cost: 0.025                                                       webapi.py:311\n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m          \u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO    \u001b[0m Billed FlexUnit cost: \u001b[1;36m0.025\u001b[0m                                                       \u001b]8;id=249905;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py\u001b\\\u001b[2mwebapi.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=268977;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py#311\u001b\\\u001b[2m311\u001b[0m\u001b]8;;\u001b\\\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
           INFO     downloading file \"output/monitor_data.hdf5\" to \"simulation_data.hdf5\"             webapi.py:593\n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m          \u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO    \u001b[0m downloading file \u001b[32m\"output/monitor_data.hdf5\"\u001b[0m to \u001b[32m\"simulation_data.hdf5\"\u001b[0m             \u001b]8;id=330550;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py\u001b\\\u001b[2mwebapi.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=751131;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py#593\u001b\\\u001b[2m593\u001b[0m\u001b]8;;\u001b\\\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
\n"
      ],
      "text/plain": [
       "\u001b[?25l"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5edb752d20bd4f66bca49e08a61a431f",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
\n",
       "
\n"
      ],
      "text/plain": [
       "\n",
       "\u001b[?25h"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
[14:48:28] INFO     loading SimulationData from simulation_data.hdf5                                  webapi.py:415\n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m[14:48:28]\u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO    \u001b[0m loading SimulationData from simulation_data.hdf5                                  \u001b]8;id=428950;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py\u001b\\\u001b[2mwebapi.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=819511;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py#415\u001b\\\u001b[2m415\u001b[0m\u001b]8;;\u001b\\\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
[14:48:29] INFO     Auto meshing using wavelength 1.4990 defined from sources.                     grid_spec.py:510\n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m[14:48:29]\u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO    \u001b[0m Auto meshing using wavelength \u001b[1;36m1.4990\u001b[0m defined from sources.                     \u001b]8;id=490077;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/components/grid/grid_spec.py\u001b\\\u001b[2mgrid_spec.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=52055;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/components/grid/grid_spec.py#510\u001b\\\u001b[2m510\u001b[0m\u001b]8;;\u001b\\\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
           INFO     Created task 'slab_adj' with task_id 'e0ffea8f-7959-40ea-93a1-8ca81e07dfa4'.      webapi.py:120\n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m          \u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO    \u001b[0m Created task \u001b[32m'slab_adj'\u001b[0m with task_id \u001b[32m'e0ffea8f-7959-40ea-93a1-8ca81e07dfa4'\u001b[0m.      \u001b]8;id=126960;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py\u001b\\\u001b[2mwebapi.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=567257;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py#120\u001b\\\u001b[2m120\u001b[0m\u001b]8;;\u001b\\\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
\n"
      ],
      "text/plain": [
       "\u001b[?25l"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "1274c9f566de40d9b60bb738f063f392",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
\n",
       "
\n"
      ],
      "text/plain": [
       "\n",
       "\u001b[?25h"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
[14:48:31] INFO     Maximum FlexUnit cost: 0.025                                                      webapi.py:253\n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m[14:48:31]\u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO    \u001b[0m Maximum FlexUnit cost: \u001b[1;36m0.025\u001b[0m                                                      \u001b]8;id=361139;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py\u001b\\\u001b[2mwebapi.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=52680;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py#253\u001b\\\u001b[2m253\u001b[0m\u001b]8;;\u001b\\\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
           INFO     status = queued                                                                   webapi.py:262\n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m          \u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO    \u001b[0m status = queued                                                                   \u001b]8;id=370755;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py\u001b\\\u001b[2mwebapi.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=895582;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py#262\u001b\\\u001b[2m262\u001b[0m\u001b]8;;\u001b\\\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
\n"
      ],
      "text/plain": [
       "\u001b[?25l"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
[14:48:34] INFO     status = preprocess                                                               webapi.py:274\n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m[14:48:34]\u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO    \u001b[0m status = preprocess                                                               \u001b]8;id=486761;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py\u001b\\\u001b[2mwebapi.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=763403;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py#274\u001b\\\u001b[2m274\u001b[0m\u001b]8;;\u001b\\\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
\n",
       "
\n"
      ],
      "text/plain": [
       "\n",
       "\u001b[?25h\r",
       "\u001b[1A\u001b[2K"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
[14:48:37] INFO     starting up solver                                                                webapi.py:278\n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m[14:48:37]\u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO    \u001b[0m starting up solver                                                                \u001b]8;id=557845;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py\u001b\\\u001b[2mwebapi.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=727832;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py#278\u001b\\\u001b[2m278\u001b[0m\u001b]8;;\u001b\\\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
[14:48:43] INFO     running solver                                                                    webapi.py:284\n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m[14:48:43]\u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO    \u001b[0m running solver                                                                    \u001b]8;id=609080;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py\u001b\\\u001b[2mwebapi.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=472430;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py#284\u001b\\\u001b[2m284\u001b[0m\u001b]8;;\u001b\\\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
\n"
      ],
      "text/plain": [
       "\u001b[?25l"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "20367e73207548cab3fde28a781158a0",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
[14:48:46] INFO     early shutoff detected, exiting.                                                  webapi.py:295\n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m[14:48:46]\u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO    \u001b[0m early shutoff detected, exiting.                                                  \u001b]8;id=125975;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py\u001b\\\u001b[2mwebapi.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=976987;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py#295\u001b\\\u001b[2m295\u001b[0m\u001b]8;;\u001b\\\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
\n",
       "
\n"
      ],
      "text/plain": [
       "\n",
       "\u001b[?25h"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
[14:48:47] INFO     status = postprocess                                                              webapi.py:301\n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m[14:48:47]\u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO    \u001b[0m status = postprocess                                                              \u001b]8;id=569252;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py\u001b\\\u001b[2mwebapi.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=974439;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py#301\u001b\\\u001b[2m301\u001b[0m\u001b]8;;\u001b\\\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
\n"
      ],
      "text/plain": [
       "\u001b[?25l"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "598779ef8097442f83ddf9d11dd705cd",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
[14:48:48] INFO     status = success                                                                  webapi.py:307\n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m[14:48:48]\u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO    \u001b[0m status = success                                                                  \u001b]8;id=993239;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py\u001b\\\u001b[2mwebapi.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=351317;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py#307\u001b\\\u001b[2m307\u001b[0m\u001b]8;;\u001b\\\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
\n",
       "
\n"
      ],
      "text/plain": [
       "\n",
       "\u001b[?25h\r",
       "\u001b[1A\u001b[2K"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
[14:48:49] INFO     Billed FlexUnit cost: 0.025                                                       webapi.py:311\n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m[14:48:49]\u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO    \u001b[0m Billed FlexUnit cost: \u001b[1;36m0.025\u001b[0m                                                       \u001b]8;id=109124;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py\u001b\\\u001b[2mwebapi.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=772746;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py#311\u001b\\\u001b[2m311\u001b[0m\u001b]8;;\u001b\\\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
           INFO     downloading file \"output/monitor_data.hdf5\" to \"simulation_data.hdf5\"             webapi.py:593\n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m          \u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO    \u001b[0m downloading file \u001b[32m\"output/monitor_data.hdf5\"\u001b[0m to \u001b[32m\"simulation_data.hdf5\"\u001b[0m             \u001b]8;id=972278;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py\u001b\\\u001b[2mwebapi.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=85871;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py#593\u001b\\\u001b[2m593\u001b[0m\u001b]8;;\u001b\\\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
\n"
      ],
      "text/plain": [
       "\u001b[?25l"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "80fff1dcaed44da391cce597b25933e0",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
\n",
       "
\n"
      ],
      "text/plain": [
       "\n",
       "\u001b[?25h"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
[14:48:51] INFO     loading SimulationData from simulation_data.hdf5                                  webapi.py:415\n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m[14:48:51]\u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO    \u001b[0m loading SimulationData from simulation_data.hdf5                                  \u001b]8;id=321421;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py\u001b\\\u001b[2mwebapi.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=284982;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/web/webapi.py#415\u001b\\\u001b[2m415\u001b[0m\u001b]8;;\u001b\\\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
[14:48:52] WARNING  'JaxSimulation.input_structures' elements 0 and 1 are overlapping or          simulation.py:131\n",
       "                    touching. Geometric gradients for overlapping structures may contain errors.                   \n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m[14:48:52]\u001b[0m\u001b[2;36m \u001b[0m\u001b[31mWARNING \u001b[0m \u001b[32m'JaxSimulation.input_structures'\u001b[0m elements \u001b[1;36m0\u001b[0m and \u001b[1;36m1\u001b[0m are overlapping or          \u001b]8;id=282221;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/plugins/adjoint/components/simulation.py\u001b\\\u001b[2msimulation.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=312888;file:///Users/twhughes/.pyenv/versions/3.10.9/lib/python3.10/site-packages/tidy3d/plugins/adjoint/components/simulation.py#131\u001b\\\u001b[2m131\u001b[0m\u001b]8;;\u001b\\\n",
       "\u001b[2;36m           \u001b[0m         touching. Geometric gradients for overlapping structures may contain errors.  \u001b[2m                 \u001b[0m\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "T_fdtd, (grad_eps_fdtd, grad_ds_fdtd) = compute_T_and_grad_fdtd(slab_eps0, slab_ds0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cbd02aa9-41f9-4e28-802d-f9a46b7f6263",
   "metadata": {},
   "source": [
    "### Checking Accuracy of TMM (Numerical) vs FDTD (Adjoint)\n",
    "\n",
    "Let's convert these from jax types to numpy arrays to work with them easier, and then display the results compared to TMM."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "41e66722-bb8c-41d9-a0a7-85009ff46df3",
   "metadata": {},
   "outputs": [],
   "source": [
    "grad_eps_fdtd = np.array(grad_eps_fdtd)\n",
    "grad_ds_fdtd = np.array(grad_ds_fdtd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "953d2497-240a-4295-9fcd-5342942983d0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T (tmm)  = 0.99731\n",
      "T (FDTD) = 0.99713\n"
     ]
    }
   ],
   "source": [
    "print(f\"T (tmm)  = {T_tmm:.5f}\")\n",
    "print(f\"T (FDTD) = {T_fdtd:.5f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "809d274a-9bb4-4f24-a7c2-962fc36f0b74",
   "metadata": {},
   "source": [
    "We see that the transmission results match very well with TMM, giving us a lot of confidence that our set up is correct.\n",
    "\n",
    "Let's look at the gradients now."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "d0e496be-a967-427d-9ed6-8eea5a96fd70",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "un-normalized:\n",
      "\tgrad_eps (tmm)  = [ 0.00353246  0.0255666   0.02079163 -0.00767556]\n",
      "\tgrad_eps (FDTD)  = [ 0.00351275  0.02560841  0.02075933 -0.00766569]\n",
      "--------------------------------------------------------------------------------\n",
      "\tgrad_ds  (tmm)  = [ 0.12389213  0.27248157  0.14586663 -0.02167071]\n",
      "\tgrad_ds  (FDTD)  = [ 0.12433368  0.2717824   0.1460508  -0.02059105]\n",
      "RMS error = 0.1682669588192957 %\n",
      "RMS error = 0.41128200939768944 %\n"
     ]
    }
   ],
   "source": [
    "print(\"un-normalized:\")\n",
    "print(f\"\\tgrad_eps (tmm)  = {grad_eps_tmm}\")\n",
    "print(f\"\\tgrad_eps (FDTD)  = {grad_eps_fdtd}\")\n",
    "print(80*'-')\n",
    "print(f\"\\tgrad_ds  (tmm)  = {grad_ds_tmm}\")\n",
    "print(f\"\\tgrad_ds  (FDTD)  = {grad_ds_fdtd}\")\n",
    "\n",
    "\n",
    "rms_eps = np.linalg.norm(grad_eps_tmm - grad_eps_fdtd) / np.linalg.norm(grad_eps_tmm)\n",
    "rms_ds = np.linalg.norm(grad_ds_tmm - grad_ds_fdtd) / np.linalg.norm(grad_ds_tmm)\n",
    "\n",
    "print(f\"RMS error = {rms_eps * 100} %\")\n",
    "print(f\"RMS error = {rms_ds * 100} %\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "111ef29c-a78f-468a-b2a7-afa3785ab5aa",
   "metadata": {},
   "source": [
    "The gradients match to < 1% of their respective norms, which is very good agreement.\n",
    "\n",
    "If we only care about the error in the \"directions\" of the gradients, we can compare their normalized versions to each other."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "2993410c-0c1d-412e-9c2c-1c43664ae20c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def normalize(arr):\n",
    "    return arr / np.linalg.norm(arr)\n",
    "\n",
    "grad_eps_tmm_norm = normalize(grad_eps_tmm)\n",
    "grad_ds_tmm_norm = normalize(grad_ds_tmm)\n",
    "grad_eps_fdtd_norm = normalize(grad_eps_fdtd)\n",
    "grad_ds_fdtd_norm = normalize(grad_ds_fdtd)\n",
    "\n",
    "rms_eps = np.linalg.norm(grad_eps_tmm_norm - grad_eps_fdtd_norm) / np.linalg.norm(grad_eps_tmm_norm)\n",
    "rms_ds = np.linalg.norm(grad_ds_tmm_norm - grad_ds_fdtd_norm) / np.linalg.norm(grad_ds_tmm_norm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "8a375cb8-79ae-4b57-86bd-26af66bba8b4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "normalized:\n",
      "\tgrad_eps (tmm)  = [ 0.10383603  0.75152497  0.61116552 -0.22562138]\n",
      "\tgrad_eps (FDTD)  = [ 0.10323393  0.75258896  0.61008249 -0.22528199]\n",
      "\tRMS error = 0.1668163643627526 %\n",
      "--------------------------------------------------------------------------------\n",
      "\tgrad_ds  (tmm)  = [ 0.37129054  0.81659613  0.43714562 -0.06494463]\n",
      "\tgrad_ds  (FDTD)  = [ 0.37305433  0.81546366  0.438215   -0.06178198]\n",
      "\tRMS error = 0.39419938518606473 %\n"
     ]
    }
   ],
   "source": [
    "print(\"normalized:\")\n",
    "print(f\"\\tgrad_eps (tmm)  = {grad_eps_tmm_norm}\")\n",
    "print(f\"\\tgrad_eps (FDTD)  = {grad_eps_fdtd_norm}\")\n",
    "print(f\"\\tRMS error = {rms_eps * 100} %\")\n",
    "print(80*'-')\n",
    "print(f\"\\tgrad_ds  (tmm)  = {grad_ds_tmm_norm}\")\n",
    "print(f\"\\tgrad_ds  (FDTD)  = {grad_ds_fdtd_norm}\")\n",
    "print(f\"\\tRMS error = {rms_ds * 100} %\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a66dbc89-3804-4576-bf08-31421fcb2476",
   "metadata": {},
   "source": [
    "In which case we see slight improvement, but the unnormalized gradients already match quite well before this."
   ]
  }
 ],
 "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": "3.10.9"
  },
  "vscode": {
   "interpreter": {
    "hash": "9e43a20ef2440406ea6cbfb61ead7c471aba2de37f508addf1f0635fad81ef64"
   }
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {
     "00b2fd25c39b41eea8d5604068d76aa0": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "2.0.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "2.0.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border_bottom": null,
       "border_left": null,
       "border_right": null,
       "border_top": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     },
     "042612d2ed0947d48a9db31c34f2729d": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/output",
       "_model_module_version": "1.0.0",
       "_model_name": "OutputModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/output",
       "_view_module_version": "1.0.0",
       "_view_name": "OutputView",
       "layout": "IPY_MODEL_00b2fd25c39b41eea8d5604068d76aa0",
       "msg_id": "",
       "outputs": [
        {
         "data": {
          "text/html": "
🚶  Starting 'slab_adj'...\n🚶  Starting 'slab_adj'...
\n",
          "text/plain": "\r\u001b[2K\u001b[32m🚶 \u001b[0m \u001b[1;32mStarting 'slab_adj'...\u001b[0m\n\u001b[32m🚶 \u001b[0m \u001b[1;32mStarting 'slab_adj'...\u001b[0m"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ],
       "tabbable": null,
       "tooltip": null
      }
     },
     "1bbefff27a0242dbb3be40be7b2f7be4": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "2.0.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "2.0.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border_bottom": null,
       "border_left": null,
       "border_right": null,
       "border_top": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     },
     "1fd505732e8a43578659ffad0816197a": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "2.0.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "2.0.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border_bottom": null,
       "border_left": null,
       "border_right": null,
       "border_top": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     },
     "2078b654416d4be3b99b1242b035b4bc": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "2.0.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "2.0.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border_bottom": null,
       "border_left": null,
       "border_right": null,
       "border_top": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     },
     "23df6bb05b614409ba70494d15633f7b": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/output",
       "_model_module_version": "1.0.0",
       "_model_name": "OutputModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/output",
       "_view_module_version": "1.0.0",
       "_view_name": "OutputView",
       "layout": "IPY_MODEL_810cf13ba5d042fe8fc4b40e55eb8261",
       "msg_id": "",
       "outputs": [
        {
         "data": {
          "text/html": "
🏃  Finishing 'slab_adj'...\n🏃  Finishing 'slab_adj'...
\n",
          "text/plain": "\r\u001b[2K\u001b[32m🏃 \u001b[0m \u001b[1;32mFinishing 'slab_adj'...\u001b[0m\n\u001b[32m🏃 \u001b[0m \u001b[1;32mFinishing 'slab_adj'...\u001b[0m"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ],
       "tabbable": null,
       "tooltip": null
      }
     },
     "2b631a8f196840f6a6128322d5723694": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/output",
       "_model_module_version": "1.0.0",
       "_model_name": "OutputModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/output",
       "_view_module_version": "1.0.0",
       "_view_name": "OutputView",
       "layout": "IPY_MODEL_2078b654416d4be3b99b1242b035b4bc",
       "msg_id": "",
       "outputs": [
        {
         "data": {
          "text/html": "
↑ simulation.json ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 0.0% • 0.0/5.7 kB • ? • -:--:--\n↑ simulation.json ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 0.0% • 0.0/5.7 kB • ? • -:--:--
\n",
          "text/plain": "\r\u001b[2K\u001b[1;31m↑\u001b[0m \u001b[1;34msimulation.json\u001b[0m \u001b[38;5;237m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m0.0%\u001b[0m • \u001b[32m0.0/5.7 kB\u001b[0m • \u001b[31m?\u001b[0m • \u001b[36m-:--:--\u001b[0m\n\u001b[1;31m↑\u001b[0m \u001b[1;34msimulation.json\u001b[0m \u001b[38;5;237m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m0.0%\u001b[0m • \u001b[32m0.0/5.7 kB\u001b[0m • \u001b[31m?\u001b[0m • \u001b[36m-:--:--\u001b[0m"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ],
       "tabbable": null,
       "tooltip": null
      }
     },
     "2bc7aad47b704edeba3d989447c6acb0": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "2.0.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "2.0.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border_bottom": null,
       "border_left": null,
       "border_right": null,
       "border_top": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     },
     "32359174e28e4358837b64156848f22a": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/output",
       "_model_module_version": "1.0.0",
       "_model_name": "OutputModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/output",
       "_view_module_version": "1.0.0",
       "_view_name": "OutputView",
       "layout": "IPY_MODEL_4b6cc865d6a94e8b9abcdcfb6719dc60",
       "msg_id": "",
       "outputs": [
        {
         "data": {
          "text/html": "
🏃  Finishing 'slab_fwd'...\n🏃  Finishing 'slab_fwd'...
\n",
          "text/plain": "\r\u001b[2K\u001b[32m🏃 \u001b[0m \u001b[1;32mFinishing 'slab_fwd'...\u001b[0m\n\u001b[32m🏃 \u001b[0m \u001b[1;32mFinishing 'slab_fwd'...\u001b[0m"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ],
       "tabbable": null,
       "tooltip": null
      }
     },
     "4b6cc865d6a94e8b9abcdcfb6719dc60": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "2.0.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "2.0.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border_bottom": null,
       "border_left": null,
       "border_right": null,
       "border_top": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     },
     "5909230a4c294168847630f8127a5c96": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/output",
       "_model_module_version": "1.0.0",
       "_model_name": "OutputModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/output",
       "_view_module_version": "1.0.0",
       "_view_name": "OutputView",
       "layout": "IPY_MODEL_d56b34370dfc4452b988c2ab43db626c",
       "msg_id": "",
       "outputs": [
        {
         "data": {
          "text/html": "
🏃  Starting 'slab_fwd'...\n🏃  Starting 'slab_fwd'...
\n",
          "text/plain": "\r\u001b[2K\u001b[32m🏃 \u001b[0m \u001b[1;32mStarting 'slab_fwd'...\u001b[0m\n\u001b[32m🏃 \u001b[0m \u001b[1;32mStarting 'slab_fwd'...\u001b[0m"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ],
       "tabbable": null,
       "tooltip": null
      }
     },
     "5b5e50ecfbfc49c189a0f0d8943171d8": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/output",
       "_model_module_version": "1.0.0",
       "_model_name": "OutputModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/output",
       "_view_module_version": "1.0.0",
       "_view_name": "OutputView",
       "layout": "IPY_MODEL_2bc7aad47b704edeba3d989447c6acb0",
       "msg_id": "",
       "outputs": [
        {
         "data": {
          "text/html": "
% done (field decay = 1.63e-10) ━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━  32% -:--:--\n% done (field decay = 1.63e-10) ━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━  32% -:--:--
\n",
          "text/plain": "\r\u001b[2K% done (field decay = 1.63e-10) \u001b[38;2;249;38;114m━━━━━━━━━━━━\u001b[0m\u001b[38;2;249;38;114m╸\u001b[0m\u001b[38;5;237m━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m 32%\u001b[0m \u001b[36m-:--:--\u001b[0m\n% done (field decay = 1.63e-10) \u001b[38;2;249;38;114m━━━━━━━━━━━━\u001b[0m\u001b[38;2;249;38;114m╸\u001b[0m\u001b[38;5;237m━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m 32%\u001b[0m \u001b[36m-:--:--\u001b[0m"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ],
       "tabbable": null,
       "tooltip": null
      }
     },
     "810cf13ba5d042fe8fc4b40e55eb8261": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "2.0.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "2.0.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border_bottom": null,
       "border_left": null,
       "border_right": null,
       "border_top": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     },
     "883016225eb74774a10a5a7a28e8791f": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/output",
       "_model_module_version": "1.0.0",
       "_model_name": "OutputModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/output",
       "_view_module_version": "1.0.0",
       "_view_name": "OutputView",
       "layout": "IPY_MODEL_bdc427d34d0440f38d8f9ba17c300d11",
       "msg_id": "",
       "outputs": [
        {
         "data": {
          "text/html": "
↑ simulation.json ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 0.0% • 0.0/5.9 kB • ? • -:--:--\n↑ simulation.json ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 0.0% • 0.0/5.9 kB • ? • -:--:--
\n",
          "text/plain": "\r\u001b[2K\u001b[1;31m↑\u001b[0m \u001b[1;34msimulation.json\u001b[0m \u001b[38;5;237m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m0.0%\u001b[0m • \u001b[32m0.0/5.9 kB\u001b[0m • \u001b[31m?\u001b[0m • \u001b[36m-:--:--\u001b[0m\n\u001b[1;31m↑\u001b[0m \u001b[1;34msimulation.json\u001b[0m \u001b[38;5;237m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m0.0%\u001b[0m • \u001b[32m0.0/5.9 kB\u001b[0m • \u001b[31m?\u001b[0m • \u001b[36m-:--:--\u001b[0m"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ],
       "tabbable": null,
       "tooltip": null
      }
     },
     "993f2741882146c8bf704caf02b82014": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "2.0.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "2.0.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border_bottom": null,
       "border_left": null,
       "border_right": null,
       "border_top": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     },
     "aff38de6b5394f53b425ace6a5d3d42e": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/output",
       "_model_module_version": "1.0.0",
       "_model_name": "OutputModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/output",
       "_view_module_version": "1.0.0",
       "_view_name": "OutputView",
       "layout": "IPY_MODEL_993f2741882146c8bf704caf02b82014",
       "msg_id": "",
       "outputs": [
        {
         "data": {
          "text/html": "
↓ monitor_data.hdf5 ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━ 93.2% • 3.4/3.7 MB • 5.5 MB/s • 0:00:01\n↓ monitor_data.hdf5 ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━ 93.2% • 3.4/3.7 MB • 5.5 MB/s • 0:00:01
\n",
          "text/plain": "\r\u001b[2K\u001b[1;32m↓\u001b[0m \u001b[1;34mmonitor_data.hdf5\u001b[0m \u001b[38;2;249;38;114m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[38;5;237m╺\u001b[0m\u001b[38;5;237m━━\u001b[0m \u001b[35m93.2%\u001b[0m • \u001b[32m3.4/3.7 MB\u001b[0m • \u001b[31m5.5 MB/s\u001b[0m • \u001b[36m0:00:01\u001b[0m\n\u001b[1;32m↓\u001b[0m \u001b[1;34mmonitor_data.hdf5\u001b[0m \u001b[38;2;249;38;114m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[38;5;237m╺\u001b[0m\u001b[38;5;237m━━\u001b[0m \u001b[35m93.2%\u001b[0m • \u001b[32m3.4/3.7 MB\u001b[0m • \u001b[31m5.5 MB/s\u001b[0m • \u001b[36m0:00:01\u001b[0m"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ],
       "tabbable": null,
       "tooltip": null
      }
     },
     "bdc427d34d0440f38d8f9ba17c300d11": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "2.0.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "2.0.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border_bottom": null,
       "border_left": null,
       "border_right": null,
       "border_top": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     },
     "d56b34370dfc4452b988c2ab43db626c": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "2.0.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "2.0.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border_bottom": null,
       "border_left": null,
       "border_right": null,
       "border_top": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     },
     "e2fbc5558c6846508566f1b9c8f87306": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/output",
       "_model_module_version": "1.0.0",
       "_model_name": "OutputModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/output",
       "_view_module_version": "1.0.0",
       "_view_name": "OutputView",
       "layout": "IPY_MODEL_1fd505732e8a43578659ffad0816197a",
       "msg_id": "",
       "outputs": [
        {
         "data": {
          "text/html": "
↓ monitor_data.hdf5 ━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━ 64.2% • 2.4/3.7 MB • 4.3 MB/s • 0:00:01\n↓ monitor_data.hdf5 ━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━ 64.2% • 2.4/3.7 MB • 4.3 MB/s • 0:00:01
\n",
          "text/plain": "\r\u001b[2K\u001b[1;32m↓\u001b[0m \u001b[1;34mmonitor_data.hdf5\u001b[0m \u001b[38;2;249;38;114m━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[38;2;249;38;114m╸\u001b[0m\u001b[38;5;237m━━━━━━━━━━━━━━\u001b[0m \u001b[35m64.2%\u001b[0m • \u001b[32m2.4/3.7 MB\u001b[0m • \u001b[31m4.3 MB/s\u001b[0m • \u001b[36m0:00:01\u001b[0m\n\u001b[1;32m↓\u001b[0m \u001b[1;34mmonitor_data.hdf5\u001b[0m \u001b[38;2;249;38;114m━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[38;2;249;38;114m╸\u001b[0m\u001b[38;5;237m━━━━━━━━━━━━━━\u001b[0m \u001b[35m64.2%\u001b[0m • \u001b[32m2.4/3.7 MB\u001b[0m • \u001b[31m4.3 MB/s\u001b[0m • \u001b[36m0:00:01\u001b[0m"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ],
       "tabbable": null,
       "tooltip": null
      }
     },
     "e901469e34ea4fa8a92892c700ce7334": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/output",
       "_model_module_version": "1.0.0",
       "_model_name": "OutputModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/output",
       "_view_module_version": "1.0.0",
       "_view_name": "OutputView",
       "layout": "IPY_MODEL_1bbefff27a0242dbb3be40be7b2f7be4",
       "msg_id": "",
       "outputs": [
        {
         "data": {
          "text/html": "
% done (field decay = 1.78e-10) ━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━  32% -:--:--\n% done (field decay = 1.78e-10) ━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━  32% -:--:--
\n",
          "text/plain": "\r\u001b[2K% done (field decay = 1.78e-10) \u001b[38;2;249;38;114m━━━━━━━━━━━━\u001b[0m\u001b[38;2;249;38;114m╸\u001b[0m\u001b[38;5;237m━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m 32%\u001b[0m \u001b[36m-:--:--\u001b[0m\n% done (field decay = 1.78e-10) \u001b[38;2;249;38;114m━━━━━━━━━━━━\u001b[0m\u001b[38;2;249;38;114m╸\u001b[0m\u001b[38;5;237m━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m 32%\u001b[0m \u001b[36m-:--:--\u001b[0m"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ],
       "tabbable": null,
       "tooltip": null
      }
     }
    },
    "version_major": 2,
    "version_minor": 0
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}