Autograd1Intro.ipynb

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    "# Autograd, automatic differentiation, and adjoint optimization: basics\n",
    "\n",
    "> Note: native autograd support is an experimental feature in tidy3d 2.7. To see the original implementation of this notebook using jax and the adjoint plugin, refer to [this notebook](https://www.flexcompute.com/tidy3d/examples/notebooks/AdjointPlugin1Intro/).\n",
    "\n",
    "## Introduction\n",
    "\n",
    "In this notebook, we will introduce the automatic differentiation feature of Tidy3D.\n",
    "This feature allows users to take derivatives of arbitrary functions involving Tidy3D simulations through the use of the \"adjoint method\".\n",
    "The advantage of the adjoint method is that the gradients can be computed using only **two** FDTD simulations, independent of the number of parameters.\n",
    "This makes it possible to do gradient-based optimization or sensitivity analysis of devices with enormous numbers of parameters with minimal computational overhead.\n",
    "For more information on the technical details of the adjoint method and what it can be used for, we recommend these references (with links to their pre-print versions):\n",
    "\n",
    "* [Gradient-based \"inverse design\" optimization in photonics](https://arxiv.org/pdf/1801.06715.pdf).\n",
    "\n",
    "* [Adjoint method for electromagnetics](https://arxiv.org/abs/1908.10507)\n",
    "\n",
    "If you want to skip to some case studies of this technique being used for some applications, see the\n",
    "\n",
    "\n",
    "* [Gradient Checking Notebook](https://www.flexcompute.com/tidy3d/examples/notebooks/Autograd2GradientChecking/).\n",
    "\n",
    "* [Inverse Design Notebook](https://www.flexcompute.com/tidy3d/examples/notebooks/Autograd3InverseDesign/).\n",
    "\n",
    "* [Multi-Objective Gradient Notebook](https://www.flexcompute.com/tidy3d/examples/notebooks/Autograd4MultiObjective/).\n",
    "\n",
    "* [Boundary Gradients Notebook](https://www.flexcompute.com/tidy3d/examples/notebooks/Autograd5BoundaryGradients/).\n",
    "\n",
    "* [Grating Coupler Notebook](https://www.flexcompute.com/tidy3d/examples/notebooks/Autograd6GratingCoupler/).\n",
    "\n",
    "\n",
    "### Function differentiation\n",
    "\n",
    "The adjoint package enables users to take derivatives of functions that involve a Tidy3D simulation. For a bit of context, let's first talk about what we mean when we talk about differentiating functions in our programs.\n",
    "Say in our program we have programmatically defined a function of one variable $f(x)$. For example:\n",
    "```py\n",
    "def f(x):\n",
    "   return x**2\n",
    "```\n",
    "\n",
    "Now, we wish to evaluate $\\frac{df(x)}{dx}$.\n",
    "\n",
    "If we know $\\frac{df}{dx}$ analytically, this is just a matter of writing a new function to compute this derivative, for example:\n",
    "\n",
    "```py\n",
    "def df(x):\n",
    "    return 2*x\n",
    "```\n",
    "However, many of the more interesting and complex functions tend to compose several sub-functions together, for example\n",
    "$$f(x) = h(y) = h(g(x))$$\n",
    "might be written in a program as\n",
    "\n",
    "```py\n",
    "def f(x):\n",
    "    y = x**2\n",
    "    return 5 * y - y**3\n",
    "```\n",
    "\n",
    "As one can imagine, defining the derivative by hand can quickly become too daunting of a task as the complexity grows.\n",
    "\n",
    "However, we can simplify things greatly with knowledge of the derivatives of the simpler functions that make up $f$.\n",
    "Following the chain rule, we can write the derivative of $f$ above as\n",
    "$$\\frac{df}{dx}=\\frac{dh}{dy}\\frac{dg}{dx}(x)$$\n",
    "\n",
    "Thus, if we know the derivatives of the composite functions $h$ and $g$, we can construct the derivative of $f$ by multiplying all of the derivatives of the composite functions.\n",
    "This idea is straightforwardly generalized to functions of several inputs and outputs, and even functions that can be written more generally as a more complex \"computational graph\" rather than a sequence of operations.\n",
    "\n",
    "### Automatic differentiation\n",
    "\n",
    "The idea of a technique called \"automatic differentiation\" is to provide a way to compute these derivatives of composite functions in programming languages both efficiently and without the user needing to define anything by hand.\n",
    "\n",
    "Automatic differentiation works by defining \"derivative rules\" for each fundamental operation that the user might incorporate in his or her function. For example, derivative rules for `h` and `g`, in the example above may be used to help define the derivative for `f`. When the function is evaluated, all of the derivative information corresponding to each operation in the function are stitched together using the chain rule to construct a derivative for the entire function. Thus, functions of arbitrary complexity can be differentiated without deriving anything beyond just the derivative rules for the most basic operations contained within.\n",
    "\n",
    "This capability is provided by many programming packages, but we chose to utilize one from the `autograd` package as it provides the flexibility and extendibility we needed for integrating this functionality into Tidy3D.\n",
    "\n",
    "Using `autograd`, we may write a function $f$ using most of the fundamental operations in python and `numpy`. In `autograd` both the operations and their derivatives are tracked when the function is called. Thus, `autograd` gives the option to apply `autograd.grad` to this function, which uses all of the derivative information and the chain rule to construct a new function that gives the derivative of the function with respect to its input arguments.\n",
    "\n",
    "In `tidy3d`, we can track functions **that involve Tidy3D simulations** in their computational graph. In essence, we privode the \"derivative\" of the `tidy3d.web.run()` function, using the adjoint method, to tell `autograd` how to differentiate functions that might involve both the setting up and postprocessing of a tidy3d simulation and its data. The end result is a framework where users can set up modeling and optimizations and utilize `autograd` automatic differentiation for optimization and sensitivity analysis efficiently and without needing to derive a single derivative rule.\n",
    "\n",
    "In his notebook, we will give an overview of how `autograd` works for beginners and provide simple example of the plugin. More complex case studies and examples will be provided in other notebooks, linked here:\n",
    "\n",
    "* [Gradient Checking Notebook](https://www.flexcompute.com/tidy3d/examples/notebooks/Autograd2GradientChecking/).\n",
    "\n",
    "* [Inverse Design Notebook](https://www.flexcompute.com/tidy3d/examples/notebooks/Autograd3InverseDesign/).\n",
    "\n",
    "* [Multi-Objective Gradient Notebook](https://www.flexcompute.com/tidy3d/examples/notebooks/Autograd4MultiObjective/).\n",
    "\n",
    "* [Boundary Gradients Notebook](https://www.flexcompute.com/tidy3d/examples/notebooks/Autograd5BoundaryGradients/).\n",
    "\n",
    "* [Grating Coupler Notebook](https://www.flexcompute.com/tidy3d/examples/notebooks/Autograd6GratingCoupler/).\n"
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    "## Automatic Differentiation using `autograd`\n",
    "\n",
    "Before jumping into any Tidy3D simulations, we will give a bit of a primer on using `autograd` for automatic differentiation. \n",
    "\n",
    "First, we will import `autograd` and its `numpy` wrapper, which provides most of the same functionality, but allows derivative tracking.\n",
    "\n",
    "Tip 1: if you run into an obscure error using `autograd`, the first thing to check is whether you're using the `autograd.numpy` wrapper instead of regular `numpy` in your function, as otherwise you will get errors from `autograd` that are not super clear."
   ]
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   "source": [
    "import autograd as ag\n",
    "import autograd.numpy as anp\n",
    "import matplotlib.pylab as plt"
   ]
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    "Say we have a function $f$ that performs several operations on a single variable.\n",
    "\n",
    "We can define this function `f` in python and also derive its derivative for this simple case, which we write as a function `df`."
   ]
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   "source": [
    "def f(x):\n",
    "    return 5 * anp.sin(x) - x**2 + x\n",
    "\n",
    "\n",
    "def df(x):\n",
    "    return 5 * anp.cos(x) - 2 * x + 1"
   ]
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   "source": [
    "Let's evaluate these functions at several points and plot them."
   ]
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   "id": "237ede5f-0a7d-45cf-927b-dcb2a9b57d9c",
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = anp.linspace(-1, 3, 1001)\n",
    "plt.plot(xs, f(xs), label=\"f(x)\")\n",
    "plt.plot(xs, df(xs), label=\"df/dx(x)\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e9915a8-59e9-4209-bf29-bd21dcda84a3",
   "metadata": {},
   "source": [
    "Now let's use autograd to compute the derivative for us and see how it compares to our analytical derivative.\n",
    "\n",
    "We first call `autograd.grad(f)`, which returns a new function that can be evaluated at `x` to give the derivative `df/dx(x)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f846ded9-26ac-4778-b637-56768b07dd6e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# get the gradient as a function of x\n",
    "df_ag = ag.grad(f)\n",
    "\n",
    "# get a set of points to feed the derivative function one by one (for now)\n",
    "xs_ag = anp.linspace(-1, 3, 21)\n",
    "df_ag_eval = [df_ag(x) for x in xs_ag]\n",
    "\n",
    "plt.plot(xs, f(xs), label=\"f(x)\")\n",
    "plt.plot(xs, df(xs), label=\"df/dx(x) [analytical]\")\n",
    "plt.plot(xs_ag, df_ag_eval, \"k.\", label=\"df/dx(x) [using autograd]\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be79405a-621a-4170-9799-ef65efc68335",
   "metadata": {},
   "source": [
    "Note: `autograd` provides several other useful gradient wrappers, which can be used in different contexts. \n",
    "\n",
    "For example `autograd.value_and_grad` returns both the function return value and the gradient value, which is useful to avoid repetitive computation if you need the value as the `autograd.grad` call must evaluate `f`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9d26f7d1-124b-4e0d-9f34-75cbf4030ad9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f_and_df = ag.value_and_grad(f)\n",
    "vals_and_grads = [f_and_df(x) for x in xs_ag]\n",
    "fs, dfs = list(zip(*vals_and_grads))\n",
    "\n",
    "plt.plot(xs_ag, fs, label=\"f(x)\")\n",
    "plt.plot(xs, df(xs), label=\"df/dx(x) [analytical]\")\n",
    "plt.plot(xs_ag, df_ag_eval, \"k.\", label=\"df/dx(x) [using autograd]\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18a7936e-9919-4ace-85bf-d8c14d124649",
   "metadata": {},
   "source": [
    "Before we continue, there are a few things to watch out for when using autograd for gradient calculation:\n",
    "\n",
    "1.  `autograd.grad` doesn't automatically convert input arguments from `int` to `float`, so avoid passing `int` types to your functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d648c131-b674-49a7-b441-ca6569e6540d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.7015115293406988\n",
      "TypeError(\"Can't differentiate w.r.t. type <class 'int'>\")\n"
     ]
    }
   ],
   "source": [
    "# ok\n",
    "print(df_ag(1.0))\n",
    "\n",
    "# errors\n",
    "try:\n",
    "    df_ag(1)\n",
    "except TypeError as e:\n",
    "    print(repr(e))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "003ef198-e0a2-495f-844e-adeff0563c1d",
   "metadata": {},
   "source": [
    "2. When differentiating with respect to several arguments, you need to tell `autograd.grad` which arguments you want to take the derivative with respect to as a tuple in indices. Otherwise it will take the derivative with respect to only the first argument."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b42164ce-41df-4bb2-8e23-eb11b2a45547",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dgdx=1.0\n",
      "dgdx=1.0, dgdy=1.0, dgdz=2.0\n"
     ]
    }
   ],
   "source": [
    "def g(x, y, z):\n",
    "    return x * y + z**2\n",
    "\n",
    "\n",
    "# only gives dg/dx\n",
    "dg = ag.grad(g)\n",
    "dgdx = dg(1.0, 1.0, 1.0)\n",
    "print(f\"dgdx={dgdx}\")\n",
    "\n",
    "# gives derivative w.r.t. all three args\n",
    "dg_all = ag.grad(g, argnum=(0, 1, 2))\n",
    "dgdx, dgdy, dgdz = dg_all(1.0, 1.0, 1.0)\n",
    "print(f\"dgdx={dgdx}, dgdy={dgdy}, dgdz={dgdz}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cbb36cd5-fef1-47d1-b25f-1fb7cc0d882b",
   "metadata": {},
   "source": [
    "## Incorporating Automatic Differentiation in `Tidy3D`\n",
    "\n",
    "With that basic introduction to automatic differentiation using `autograd`, we can now show how `Tidy3D` lets us do the same thing but where our functions can now involve setting up, running, and postprocessing a `tidy3d.Simulation`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "f304ea94-34df-4741-ab99-87003884eee7",
   "metadata": {},
   "outputs": [],
   "source": [
    "import tidy3d as td\n",
    "\n",
    "td.config.logging_level = \"INFO\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e54cc9fa-b5f2-4f62-b31e-3a0e1fa7acac",
   "metadata": {},
   "source": [
    "### Simulation example\n",
    "\n",
    "In our example, we will set up a function that involves a simulation of transmission through a waveguide in the presence of a scatterer.\n",
    "\n",
    "This scatterer geometry and material properties will depend on the function input arguments.\n",
    "\n",
    "The output of the function will simply be the power transmitted into the 0th order mode.\n",
    "\n",
    "We will then take the gradient of the output of this function (power) with respect to the scatterer geometric and medium properties using `autograd`.\n",
    "\n",
    "To start, it can often be helpful to break our function up into a few parts for debugging.\n",
    "\n",
    "Therefore, we will introduce one function to make the `td.Simulation` given the input arguments and one function to postprocess the result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "3cbe5188-a552-40db-a1e6-ddb4af0ead63",
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_simulation(center: tuple, size: tuple, eps: float) -> td.Simulation:\n",
    "    \"\"\"Makes a simulation with a variable scatter width, height, and relative permittivity.\"\"\"\n",
    "\n",
    "    wavelength = 1.0\n",
    "    freq0 = td.C_0 / wavelength\n",
    "    dl = 0.02\n",
    "\n",
    "    # a \"static\" structure\n",
    "    waveguide = td.Structure(\n",
    "        geometry=td.Box(size=(td.inf, 0.3, 0.2)), medium=td.Medium(permittivity=2.0)\n",
    "    )\n",
    "\n",
    "    # our \"forward\" soruce\n",
    "    mode_src = td.ModeSource(\n",
    "        size=(0, 1.5, 1.5),\n",
    "        center=(-0.9, 0, 0),\n",
    "        mode_index=0,\n",
    "        source_time=td.GaussianPulse(freq0=freq0, fwidth=freq0 / 10),\n",
    "        direction=\"+\",\n",
    "    )\n",
    "\n",
    "    # a monitor to store data that our overall function will depend on\n",
    "    mode_mnt = td.ModeMonitor(\n",
    "        size=(0, 1.5, 1.5),\n",
    "        center=(+0.9, 0, 0),\n",
    "        mode_spec=mode_src.mode_spec,\n",
    "        freqs=[freq0],\n",
    "        name=\"mode\",\n",
    "    )\n",
    "\n",
    "    # the structure that depends on the input parameters, which we will differentiate our function w.r.t\n",
    "    scatterer = td.Structure(\n",
    "        geometry=td.Box(\n",
    "            center=center,\n",
    "            size=size,\n",
    "        ),\n",
    "        medium=td.Medium(permittivity=eps),\n",
    "    )\n",
    "\n",
    "    return td.Simulation(\n",
    "        size=(2, 2, 2),\n",
    "        run_time=1e-12,\n",
    "        structures=[waveguide, scatterer],\n",
    "        sources=[mode_src],\n",
    "        monitors=[mode_mnt],\n",
    "        boundary_spec=td.BoundarySpec.all_sides(td.PML()),\n",
    "        grid_spec=td.GridSpec.uniform(dl=dl),\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4dcb88e-490f-4579-bb7d-4166bd6a3be5",
   "metadata": {},
   "source": [
    "\n",
    "Let's try setting up the simulation and plotting it for starters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "f4da7dc4-b13b-4c62-8590-4877ed71422a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# starting set of input parameters\n",
    "center0 = (0.0, 0.0, 0.0)\n",
    "size0 = (0.5, 1.0, 1.0)\n",
    "eps0 = 3.0\n",
    "\n",
    "sim = make_simulation(center=center0, size=size0, eps=eps0)\n",
    "_, axes = plt.subplots(1, 3, figsize=(16, 5))\n",
    "\n",
    "for ax, dim in zip(axes, \"xyz\"):\n",
    "    sim.plot(**{dim: 0}, ax=ax)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a390df41-e293-4dbf-83e0-f5dff8e700cc",
   "metadata": {},
   "source": [
    "### Post-processing the output data\n",
    "\n",
    "After the simulation is run, it returns a `td.SimulationData` containing the data we want to post-process.\n",
    "\n",
    "Let's write a function that will process this `td.SimulationData` and return the power in the mode amplitude of our output mode monitor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "5d5c14b9-cb22-4ced-aad8-834b29c5800b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_power(sim_data: td.SimulationData) -> float:\n",
    "    \"\"\"Post process the result of the Simulation run to return the power in the mode at index=0.\"\"\"\n",
    "\n",
    "    freq0 = sim_data.simulation.monitors[0].freqs[0]\n",
    "    mode_data = sim_data[\"mode\"]\n",
    "    mode_amps = mode_data.amps\n",
    "    amp = mode_amps.sel(direction=\"+\", f=freq0, mode_index=0).values\n",
    "    return anp.sum(abs(amp) ** 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a49d64c6-7591-4b8b-bfa3-d09c1501d4b0",
   "metadata": {},
   "source": [
    "### Defining the tidy3d simulation function for differentiation\n",
    "\n",
    "Next, we can import the `tidy3d..web.run` function and put all the pieces together into a single function to compute the 0th order transmitted power as a function of `center`, `size`, and `eps` (relative permittivty) of the scatterer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "7257472c-5db1-4b93-8cdb-24b3cc32775d",
   "metadata": {
    "tags": []
   },
   "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\">11:43:14 CEST </span>INFO: env_key is <span style=\"color: #800080; text-decoration-color: #800080; font-style: italic\">None</span>                                             \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m11:43:14 CEST\u001b[0m\u001b[2;36m \u001b[0mINFO: env_key is \u001b[3;35mNone\u001b[0m                                             \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import tidy3d.web as web"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "c5e5e42e-dc9f-4e01-b39b-2f2f9f1bb680",
   "metadata": {},
   "outputs": [],
   "source": [
    "def power(center: tuple, size: tuple, eps: float) -> float:\n",
    "    \"\"\"Compute power transmitted into 0th order mode given a set of scatterer parameters.\"\"\"\n",
    "    sim = make_simulation(center=center, size=size, eps=eps)\n",
    "    sim_data = web.run(sim, task_name=\"autograd 1\")\n",
    "    return compute_power(sim_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "a89d7ff4-19c4-484e-824c-504654a71a91",
   "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\">11:43:24 CEST </span>Created task <span style=\"color: #008000; text-decoration-color: #008000\">'autograd 1'</span> with task_id                            \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span><span style=\"color: #008000; text-decoration-color: #008000\">'fdve-0b1bd55e-e5dd-4bb6-820e-d3c85e0e8b21'</span> and task_type <span style=\"color: #008000; text-decoration-color: #008000\">'FDTD'</span>. \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m11:43:24 CEST\u001b[0m\u001b[2;36m \u001b[0mCreated task \u001b[32m'autograd 1'\u001b[0m with task_id                            \n",
       "\u001b[2;36m              \u001b[0m\u001b[32m'fdve-0b1bd55e-e5dd-4bb6-820e-d3c85e0e8b21'\u001b[0m and task_type \u001b[32m'FDTD'\u001b[0m. \n"
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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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\"><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-0b1bd55e-e5dd-4bb6-820e-d3c85e0e8b21\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-0b1bd55e-e5</span></a>\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-0b1bd55e-e5dd-4bb6-820e-d3c85e0e8b21\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">dd-4bb6-820e-d3c85e0e8b21'</span></a>.                                       \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=150971;https://tidy3d.simulation.cloud/workbench?taskId=fdve-0b1bd55e-e5dd-4bb6-820e-d3c85e0e8b21\u001b\\\u001b[32m'https://tidy3d.simulation.cloud/workbench?\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=491472;https://tidy3d.simulation.cloud/workbench?taskId=fdve-0b1bd55e-e5dd-4bb6-820e-d3c85e0e8b21\u001b\\\u001b[32mtaskId\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=150971;https://tidy3d.simulation.cloud/workbench?taskId=fdve-0b1bd55e-e5dd-4bb6-820e-d3c85e0e8b21\u001b\\\u001b[32m=\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=23130;https://tidy3d.simulation.cloud/workbench?taskId=fdve-0b1bd55e-e5dd-4bb6-820e-d3c85e0e8b21\u001b\\\u001b[32mfdve\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=150971;https://tidy3d.simulation.cloud/workbench?taskId=fdve-0b1bd55e-e5dd-4bb6-820e-d3c85e0e8b21\u001b\\\u001b[32m-0b1bd55e-e5\u001b[0m\u001b]8;;\u001b\\\n",
       "\u001b[2;36m              \u001b[0m\u001b]8;id=150971;https://tidy3d.simulation.cloud/workbench?taskId=fdve-0b1bd55e-e5dd-4bb6-820e-d3c85e0e8b21\u001b\\\u001b[32mdd-4bb6-820e-d3c85e0e8b21'\u001b[0m\u001b]8;;\u001b\\.                                       \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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       "model_id": "e7d641f84adb47678f7173b83dfc3f2f",
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      "text/plain": [
       "Output()"
      ]
     },
     "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\"></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\">11:43:33 CEST </span>status = queued                                                   \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m11:43:33 CEST\u001b[0m\u001b[2;36m \u001b[0mstatus = queued                                                   \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>To cancel the simulation, use <span style=\"color: #008000; text-decoration-color: #008000\">'web.abort(task_id)'</span> or             \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span><span style=\"color: #008000; text-decoration-color: #008000\">'web.delete(task_id)'</span> or abort/delete the task in the web UI.     \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span>Terminating the Python script will not stop the job running on the\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span>cloud.                                                            \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m             \u001b[0m\u001b[2;36m \u001b[0mTo cancel the simulation, use \u001b[32m'web.abort\u001b[0m\u001b[32m(\u001b[0m\u001b[32mtask_id\u001b[0m\u001b[32m)\u001b[0m\u001b[32m'\u001b[0m or             \n",
       "\u001b[2;36m              \u001b[0m\u001b[32m'web.delete\u001b[0m\u001b[32m(\u001b[0m\u001b[32mtask_id\u001b[0m\u001b[32m)\u001b[0m\u001b[32m'\u001b[0m or abort/delete the task in the web UI.     \n",
       "\u001b[2;36m              \u001b[0mTerminating the Python script will not stop the job running on the\n",
       "\u001b[2;36m              \u001b[0mcloud.                                                            \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b5a2eca301e44066ae0f532fd54e93c5",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "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\">11:43:59 CEST </span>status = preprocess                                               \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m11:43:59 CEST\u001b[0m\u001b[2;36m \u001b[0mstatus = preprocess                                               \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\"></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\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">11:44:00 CEST </span>Maximum FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.025</span>. Use <span style=\"color: #008000; text-decoration-color: #008000\">'web.real_cost(task_id)'</span> to   \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span>get the billed FlexCredit cost after a simulation run.            \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m11:44:00 CEST\u001b[0m\u001b[2;36m \u001b[0mMaximum FlexCredit cost: \u001b[1;36m0.025\u001b[0m. Use \u001b[32m'web.real_cost\u001b[0m\u001b[32m(\u001b[0m\u001b[32mtask_id\u001b[0m\u001b[32m)\u001b[0m\u001b[32m'\u001b[0m to   \n",
       "\u001b[2;36m              \u001b[0mget the billed FlexCredit cost after a simulation run.            \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>starting up solver                                                \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m             \u001b[0m\u001b[2;36m \u001b[0mstarting up solver                                                \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>running solver                                                    \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m             \u001b[0m\u001b[2;36m \u001b[0mrunning solver                                                    \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b925c7eb6f154a30828d709d21900a93",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "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\">11:44:05 CEST </span>early shutoff detected at <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">8</span>%, exiting.                            \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m11:44:05 CEST\u001b[0m\u001b[2;36m \u001b[0mearly shutoff detected at \u001b[1;36m8\u001b[0m%, exiting.                            \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\"></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\">              </span>status = success                                                  \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m             \u001b[0m\u001b[2;36m \u001b[0mstatus = success                                                  \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\"></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\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span>View simulation result at                                         \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-0b1bd55e-e5dd-4bb6-820e-d3c85e0e8b21\" target=\"_blank\"><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-0b1bd55e-e5</span></a>\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-0b1bd55e-e5dd-4bb6-820e-d3c85e0e8b21\" target=\"_blank\"><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">dd-4bb6-820e-d3c85e0e8b21'</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 simulation result at                                         \n",
       "\u001b[2;36m              \u001b[0m\u001b]8;id=23383;https://tidy3d.simulation.cloud/workbench?taskId=fdve-0b1bd55e-e5dd-4bb6-820e-d3c85e0e8b21\u001b\\\u001b[4;34m'https://tidy3d.simulation.cloud/workbench?\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=78547;https://tidy3d.simulation.cloud/workbench?taskId=fdve-0b1bd55e-e5dd-4bb6-820e-d3c85e0e8b21\u001b\\\u001b[4;34mtaskId\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=23383;https://tidy3d.simulation.cloud/workbench?taskId=fdve-0b1bd55e-e5dd-4bb6-820e-d3c85e0e8b21\u001b\\\u001b[4;34m=\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=334330;https://tidy3d.simulation.cloud/workbench?taskId=fdve-0b1bd55e-e5dd-4bb6-820e-d3c85e0e8b21\u001b\\\u001b[4;34mfdve\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=23383;https://tidy3d.simulation.cloud/workbench?taskId=fdve-0b1bd55e-e5dd-4bb6-820e-d3c85e0e8b21\u001b\\\u001b[4;34m-0b1bd55e-e5\u001b[0m\u001b]8;;\u001b\\\n",
       "\u001b[2;36m              \u001b[0m\u001b]8;id=23383;https://tidy3d.simulation.cloud/workbench?taskId=fdve-0b1bd55e-e5dd-4bb6-820e-d3c85e0e8b21\u001b\\\u001b[4;34mdd-4bb6-820e-d3c85e0e8b21'\u001b[0m\u001b]8;;\u001b\\\u001b[4;34m.\u001b[0m                                       \n"
      ]
     },
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      "text/plain": [
       "Output()"
      ]
     },
     "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\"></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\">11:44:07 CEST </span>loading simulation from simulation_data.hdf5                      \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m11:44:07 CEST\u001b[0m\u001b[2;36m \u001b[0mloading simulation from simulation_data.hdf5                      \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "0.5520313810023142"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "power(center0, size0, eps0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90ee44c1-38a6-4dba-add5-9b36c43454cb",
   "metadata": {},
   "source": [
    "### Running and differentiating the simulation using `autograd`\n",
    "\n",
    "Finally, using the `autograd` tools described earlier, we can differentiate this `power` function. \n",
    "\n",
    "For demonstration, let's use `autograd.value_and_grad` to both compute the power **and** the gradient w.r.t. each of the 3 input parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "8a6518dd-c5a9-4826-95f6-7a0ed90e2f9a",
   "metadata": {},
   "outputs": [],
   "source": [
    "d_power = ag.value_and_grad(power, argnum=(0, 1, 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f787405-1c6e-40b1-81d2-1a64d667e009",
   "metadata": {},
   "source": [
    "We will run this function and assign variables to the power values and the gradients returned.\n",
    "\n",
    "Note that running this will set off **two** separate tasks, one after another, called, `\"adjoint_power_fwd\"` and `\"adjoint_power_adj\"`.\n",
    "\n",
    "The first is evaluating our simulation in \"forward mode\", computing the power and stashing information needed for gradient computation.\n",
    "\n",
    "The second step runs the \"adjoint\" simulation, in which the output monitor is converted to a source and the simulation is re-run.\n",
    "\n",
    "The results of both of these simulations runs are combined behind the scene to tell `autograd` how to compute the gradient for us."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "68f34dce-3504-4dba-8012-436c4ff21ecc",
   "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\">11:44:23 CEST </span>INFO: running primitive <span style=\"color: #008000; text-decoration-color: #008000\">'_run_primitive()'</span>                        \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m11:44:23 CEST\u001b[0m\u001b[2;36m \u001b[0mINFO: running primitive \u001b[32m'_run_primitive\u001b[0m\u001b[32m(\u001b[0m\u001b[32m)\u001b[0m\u001b[32m'\u001b[0m                        \n"
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     },
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     "output_type": "display_data"
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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>INFO: running regular simulation with <span style=\"color: #008000; text-decoration-color: #008000\">'_run_tidy3d()'</span>             \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m             \u001b[0m\u001b[2;36m \u001b[0mINFO: running regular simulation with \u001b[32m'_run_tidy3d\u001b[0m\u001b[32m(\u001b[0m\u001b[32m)\u001b[0m\u001b[32m'\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>Created task <span style=\"color: #008000; text-decoration-color: #008000\">'autograd 1'</span> with task_id                            \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span><span style=\"color: #008000; text-decoration-color: #008000\">'fdve-09e01802-8b37-43eb-8c02-3ad08a8abaf5'</span> and task_type <span style=\"color: #008000; text-decoration-color: #008000\">'FDTD'</span>. \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m             \u001b[0m\u001b[2;36m \u001b[0mCreated task \u001b[32m'autograd 1'\u001b[0m with task_id                            \n",
       "\u001b[2;36m              \u001b[0m\u001b[32m'fdve-09e01802-8b37-43eb-8c02-3ad08a8abaf5'\u001b[0m and task_type \u001b[32m'FDTD'\u001b[0m. \n"
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     },
     "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-09e01802-8b37-43eb-8c02-3ad08a8abaf5\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-09e01802-8b</span></a>\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-09e01802-8b37-43eb-8c02-3ad08a8abaf5\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">37-43eb-8c02-3ad08a8abaf5'</span></a>.                                       \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=216935;https://tidy3d.simulation.cloud/workbench?taskId=fdve-09e01802-8b37-43eb-8c02-3ad08a8abaf5\u001b\\\u001b[32m'https://tidy3d.simulation.cloud/workbench?\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=513165;https://tidy3d.simulation.cloud/workbench?taskId=fdve-09e01802-8b37-43eb-8c02-3ad08a8abaf5\u001b\\\u001b[32mtaskId\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=216935;https://tidy3d.simulation.cloud/workbench?taskId=fdve-09e01802-8b37-43eb-8c02-3ad08a8abaf5\u001b\\\u001b[32m=\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=78033;https://tidy3d.simulation.cloud/workbench?taskId=fdve-09e01802-8b37-43eb-8c02-3ad08a8abaf5\u001b\\\u001b[32mfdve\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=216935;https://tidy3d.simulation.cloud/workbench?taskId=fdve-09e01802-8b37-43eb-8c02-3ad08a8abaf5\u001b\\\u001b[32m-09e01802-8b\u001b[0m\u001b]8;;\u001b\\\n",
       "\u001b[2;36m              \u001b[0m\u001b]8;id=216935;https://tidy3d.simulation.cloud/workbench?taskId=fdve-09e01802-8b37-43eb-8c02-3ad08a8abaf5\u001b\\\u001b[32m37-43eb-8c02-3ad08a8abaf5'\u001b[0m\u001b]8;;\u001b\\.                                       \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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       "model_id": "b96c2c945e884d2993c6cbf7bbd13fe4",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "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\"></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\">11:44:26 CEST </span>status = queued                                                   \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m11:44:26 CEST\u001b[0m\u001b[2;36m \u001b[0mstatus = queued                                                   \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>To cancel the simulation, use <span style=\"color: #008000; text-decoration-color: #008000\">'web.abort(task_id)'</span> or             \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span><span style=\"color: #008000; text-decoration-color: #008000\">'web.delete(task_id)'</span> or abort/delete the task in the web UI.     \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span>Terminating the Python script will not stop the job running on the\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span>cloud.                                                            \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m             \u001b[0m\u001b[2;36m \u001b[0mTo cancel the simulation, use \u001b[32m'web.abort\u001b[0m\u001b[32m(\u001b[0m\u001b[32mtask_id\u001b[0m\u001b[32m)\u001b[0m\u001b[32m'\u001b[0m or             \n",
       "\u001b[2;36m              \u001b[0m\u001b[32m'web.delete\u001b[0m\u001b[32m(\u001b[0m\u001b[32mtask_id\u001b[0m\u001b[32m)\u001b[0m\u001b[32m'\u001b[0m or abort/delete the task in the web UI.     \n",
       "\u001b[2;36m              \u001b[0mTerminating the Python script will not stop the job running on the\n",
       "\u001b[2;36m              \u001b[0mcloud.                                                            \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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       "model_id": "01853036b54d445a9d9b6fd83d4f16d5",
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       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "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\">11:44:29 CEST </span>status = preprocess                                               \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m11:44:29 CEST\u001b[0m\u001b[2;36m \u001b[0mstatus = preprocess                                               \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\"></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\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">11:44:31 CEST </span>Maximum FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.025</span>. Use <span style=\"color: #008000; text-decoration-color: #008000\">'web.real_cost(task_id)'</span> to   \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span>get the billed FlexCredit cost after a simulation run.            \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m11:44:31 CEST\u001b[0m\u001b[2;36m \u001b[0mMaximum FlexCredit cost: \u001b[1;36m0.025\u001b[0m. Use \u001b[32m'web.real_cost\u001b[0m\u001b[32m(\u001b[0m\u001b[32mtask_id\u001b[0m\u001b[32m)\u001b[0m\u001b[32m'\u001b[0m to   \n",
       "\u001b[2;36m              \u001b[0mget the billed FlexCredit cost after a simulation run.            \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>starting up solver                                                \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m             \u001b[0m\u001b[2;36m \u001b[0mstarting up solver                                                \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>running solver                                                    \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m             \u001b[0m\u001b[2;36m \u001b[0mrunning solver                                                    \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e8d92885a7874c439856e2d3a60ed611",
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       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "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\">11:44:36 CEST </span>early shutoff detected at <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">8</span>%, exiting.                            \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m11:44:36 CEST\u001b[0m\u001b[2;36m \u001b[0mearly shutoff detected at \u001b[1;36m8\u001b[0m%, exiting.                            \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\"></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\">              </span>status = postprocess                                              \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m             \u001b[0m\u001b[2;36m \u001b[0mstatus = postprocess                                              \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "145f460a4fce49efb429d16bc588be04",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "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\">11:44:39 CEST </span>status = success                                                  \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m11:44:39 CEST\u001b[0m\u001b[2;36m \u001b[0mstatus = success                                                  \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\"></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\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span>View simulation result at                                         \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-09e01802-8b37-43eb-8c02-3ad08a8abaf5\" target=\"_blank\"><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-09e01802-8b</span></a>\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-09e01802-8b37-43eb-8c02-3ad08a8abaf5\" target=\"_blank\"><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">37-43eb-8c02-3ad08a8abaf5'</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 simulation result at                                         \n",
       "\u001b[2;36m              \u001b[0m\u001b]8;id=888800;https://tidy3d.simulation.cloud/workbench?taskId=fdve-09e01802-8b37-43eb-8c02-3ad08a8abaf5\u001b\\\u001b[4;34m'https://tidy3d.simulation.cloud/workbench?\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=809692;https://tidy3d.simulation.cloud/workbench?taskId=fdve-09e01802-8b37-43eb-8c02-3ad08a8abaf5\u001b\\\u001b[4;34mtaskId\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=888800;https://tidy3d.simulation.cloud/workbench?taskId=fdve-09e01802-8b37-43eb-8c02-3ad08a8abaf5\u001b\\\u001b[4;34m=\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=285881;https://tidy3d.simulation.cloud/workbench?taskId=fdve-09e01802-8b37-43eb-8c02-3ad08a8abaf5\u001b\\\u001b[4;34mfdve\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=888800;https://tidy3d.simulation.cloud/workbench?taskId=fdve-09e01802-8b37-43eb-8c02-3ad08a8abaf5\u001b\\\u001b[4;34m-09e01802-8b\u001b[0m\u001b]8;;\u001b\\\n",
       "\u001b[2;36m              \u001b[0m\u001b]8;id=888800;https://tidy3d.simulation.cloud/workbench?taskId=fdve-09e01802-8b37-43eb-8c02-3ad08a8abaf5\u001b\\\u001b[4;34m37-43eb-8c02-3ad08a8abaf5'\u001b[0m\u001b]8;;\u001b\\\u001b[4;34m.\u001b[0m                                       \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "421484c6ce744e19b7990b92dc255997",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "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\"></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\">11:44:42 CEST </span>loading simulation from simulation_data.hdf5                      \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m11:44:42 CEST\u001b[0m\u001b[2;36m \u001b[0mloading simulation from simulation_data.hdf5                      \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>INFO:  -&gt; <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1</span> monitors, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1</span> adjoint field monitors, <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1</span> adjoint eps     \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span>monitors.                                                         \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m             \u001b[0m\u001b[2;36m \u001b[0mINFO:  -> \u001b[1;36m1\u001b[0m monitors, \u001b[1;36m1\u001b[0m adjoint field monitors, \u001b[1;36m1\u001b[0m adjoint eps     \n",
       "\u001b[2;36m              \u001b[0mmonitors.                                                         \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>INFO: constructing custom vjp function for backwards pass.        \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m             \u001b[0m\u001b[2;36m \u001b[0mINFO: constructing custom vjp function for backwards pass.        \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>INFO: Running custom vjp <span style=\"font-weight: bold\">(</span>adjoint<span style=\"font-weight: bold\">)</span> pipeline.                      \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m             \u001b[0m\u001b[2;36m \u001b[0mINFO: Running custom vjp \u001b[1m(\u001b[0madjoint\u001b[1m)\u001b[0m pipeline.                      \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>INFO: Adjoint simulation created with <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1</span> sources.                  \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m             \u001b[0m\u001b[2;36m \u001b[0mINFO: Adjoint simulation created with \u001b[1;36m1\u001b[0m sources.                  \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>INFO: running regular simulation with <span style=\"color: #008000; text-decoration-color: #008000\">'_run_tidy3d()'</span>             \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m             \u001b[0m\u001b[2;36m \u001b[0mINFO: running regular simulation with \u001b[32m'_run_tidy3d\u001b[0m\u001b[32m(\u001b[0m\u001b[32m)\u001b[0m\u001b[32m'\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>Created task <span style=\"color: #008000; text-decoration-color: #008000\">'autograd 1_adjoint'</span> with task_id                    \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span><span style=\"color: #008000; text-decoration-color: #008000\">'fdve-d1e1552d-0cba-4431-91e7-1e294ce5b7f7'</span> and task_type <span style=\"color: #008000; text-decoration-color: #008000\">'FDTD'</span>. \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m             \u001b[0m\u001b[2;36m \u001b[0mCreated task \u001b[32m'autograd 1_adjoint'\u001b[0m with task_id                    \n",
       "\u001b[2;36m              \u001b[0m\u001b[32m'fdve-d1e1552d-0cba-4431-91e7-1e294ce5b7f7'\u001b[0m and task_type \u001b[32m'FDTD'\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-d1e1552d-0cba-4431-91e7-1e294ce5b7f7\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-d1e1552d-0c</span></a>\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-d1e1552d-0cba-4431-91e7-1e294ce5b7f7\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">ba-4431-91e7-1e294ce5b7f7'</span></a>.                                       \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=355745;https://tidy3d.simulation.cloud/workbench?taskId=fdve-d1e1552d-0cba-4431-91e7-1e294ce5b7f7\u001b\\\u001b[32m'https://tidy3d.simulation.cloud/workbench?\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=129818;https://tidy3d.simulation.cloud/workbench?taskId=fdve-d1e1552d-0cba-4431-91e7-1e294ce5b7f7\u001b\\\u001b[32mtaskId\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=355745;https://tidy3d.simulation.cloud/workbench?taskId=fdve-d1e1552d-0cba-4431-91e7-1e294ce5b7f7\u001b\\\u001b[32m=\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=732148;https://tidy3d.simulation.cloud/workbench?taskId=fdve-d1e1552d-0cba-4431-91e7-1e294ce5b7f7\u001b\\\u001b[32mfdve\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=355745;https://tidy3d.simulation.cloud/workbench?taskId=fdve-d1e1552d-0cba-4431-91e7-1e294ce5b7f7\u001b\\\u001b[32m-d1e1552d-0c\u001b[0m\u001b]8;;\u001b\\\n",
       "\u001b[2;36m              \u001b[0m\u001b]8;id=355745;https://tidy3d.simulation.cloud/workbench?taskId=fdve-d1e1552d-0cba-4431-91e7-1e294ce5b7f7\u001b\\\u001b[32mba-4431-91e7-1e294ce5b7f7'\u001b[0m\u001b]8;;\u001b\\.                                       \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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       "version_minor": 0
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      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
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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"
      ],
      "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\">11:44:44 CEST </span>status = queued                                                   \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m11:44:44 CEST\u001b[0m\u001b[2;36m \u001b[0mstatus = queued                                                   \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>To cancel the simulation, use <span style=\"color: #008000; text-decoration-color: #008000\">'web.abort(task_id)'</span> or             \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span><span style=\"color: #008000; text-decoration-color: #008000\">'web.delete(task_id)'</span> or abort/delete the task in the web UI.     \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span>Terminating the Python script will not stop the job running on the\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span>cloud.                                                            \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m             \u001b[0m\u001b[2;36m \u001b[0mTo cancel the simulation, use \u001b[32m'web.abort\u001b[0m\u001b[32m(\u001b[0m\u001b[32mtask_id\u001b[0m\u001b[32m)\u001b[0m\u001b[32m'\u001b[0m or             \n",
       "\u001b[2;36m              \u001b[0m\u001b[32m'web.delete\u001b[0m\u001b[32m(\u001b[0m\u001b[32mtask_id\u001b[0m\u001b[32m)\u001b[0m\u001b[32m'\u001b[0m or abort/delete the task in the web UI.     \n",
       "\u001b[2;36m              \u001b[0mTerminating the Python script will not stop the job running on the\n",
       "\u001b[2;36m              \u001b[0mcloud.                                                            \n"
      ]
     },
     "metadata": {},
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       "Output()"
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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\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">11:44:47 CEST </span>status = preprocess                                               \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m11:44:47 CEST\u001b[0m\u001b[2;36m \u001b[0mstatus = preprocess                                               \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\"></pre>\n"
      ],
      "text/plain": []
     },
     "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\">11:44:50 CEST </span>Maximum FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.025</span>. Use <span style=\"color: #008000; text-decoration-color: #008000\">'web.real_cost(task_id)'</span> to   \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span>get the billed FlexCredit cost after a simulation run.            \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m11:44:50 CEST\u001b[0m\u001b[2;36m \u001b[0mMaximum FlexCredit cost: \u001b[1;36m0.025\u001b[0m. Use \u001b[32m'web.real_cost\u001b[0m\u001b[32m(\u001b[0m\u001b[32mtask_id\u001b[0m\u001b[32m)\u001b[0m\u001b[32m'\u001b[0m to   \n",
       "\u001b[2;36m              \u001b[0mget the billed FlexCredit cost after a simulation run.            \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>starting up solver                                                \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m             \u001b[0m\u001b[2;36m \u001b[0mstarting up solver                                                \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>running solver                                                    \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m             \u001b[0m\u001b[2;36m \u001b[0mrunning solver                                                    \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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    {
     "data": {
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       "Output()"
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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\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">11:44:54 CEST </span>early shutoff detected at <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">8</span>%, exiting.                            \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m11:44:54 CEST\u001b[0m\u001b[2;36m \u001b[0mearly shutoff detected at \u001b[1;36m8\u001b[0m%, exiting.                            \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\"></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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    {
     "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>status = postprocess                                              \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m             \u001b[0m\u001b[2;36m \u001b[0mstatus = postprocess                                              \n"
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       "Output()"
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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\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">11:44:58 CEST </span>status = success                                                  \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m11:44:58 CEST\u001b[0m\u001b[2;36m \u001b[0mstatus = success                                                  \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\"></pre>\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\">11:44:59 CEST </span>View simulation result at                                         \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-d1e1552d-0cba-4431-91e7-1e294ce5b7f7\" target=\"_blank\"><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-d1e1552d-0c</span></a>\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-d1e1552d-0cba-4431-91e7-1e294ce5b7f7\" target=\"_blank\"><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">ba-4431-91e7-1e294ce5b7f7'</span></a><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">.</span>                                       \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m11:44:59 CEST\u001b[0m\u001b[2;36m \u001b[0mView simulation result at                                         \n",
       "\u001b[2;36m              \u001b[0m\u001b]8;id=110531;https://tidy3d.simulation.cloud/workbench?taskId=fdve-d1e1552d-0cba-4431-91e7-1e294ce5b7f7\u001b\\\u001b[4;34m'https://tidy3d.simulation.cloud/workbench?\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=510436;https://tidy3d.simulation.cloud/workbench?taskId=fdve-d1e1552d-0cba-4431-91e7-1e294ce5b7f7\u001b\\\u001b[4;34mtaskId\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=110531;https://tidy3d.simulation.cloud/workbench?taskId=fdve-d1e1552d-0cba-4431-91e7-1e294ce5b7f7\u001b\\\u001b[4;34m=\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=797211;https://tidy3d.simulation.cloud/workbench?taskId=fdve-d1e1552d-0cba-4431-91e7-1e294ce5b7f7\u001b\\\u001b[4;34mfdve\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=110531;https://tidy3d.simulation.cloud/workbench?taskId=fdve-d1e1552d-0cba-4431-91e7-1e294ce5b7f7\u001b\\\u001b[4;34m-d1e1552d-0c\u001b[0m\u001b]8;;\u001b\\\n",
       "\u001b[2;36m              \u001b[0m\u001b]8;id=110531;https://tidy3d.simulation.cloud/workbench?taskId=fdve-d1e1552d-0cba-4431-91e7-1e294ce5b7f7\u001b\\\u001b[4;34mba-4431-91e7-1e294ce5b7f7'\u001b[0m\u001b]8;;\u001b\\\u001b[4;34m.\u001b[0m                                       \n"
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       "</pre>\n"
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       "\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\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">11:45:06 CEST </span>loading simulation from simulation_data.hdf5                      \n",
       "</pre>\n"
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       "\u001b[2;36m11:45:06 CEST\u001b[0m\u001b[2;36m \u001b[0mloading simulation from simulation_data.hdf5                      \n"
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   ],
   "source": [
    "power_value, (dp_dcenter, dp_dsize, dp_deps) = d_power(center0, size0, eps0)"
   ]
  },
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   "cell_type": "markdown",
   "id": "0ac63a75-89de-42c5-929d-f46da6f22864",
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    "> Note: the gradient evaluation functions returned by `autograd.grad()` do not accept keyword arguments (ie. `center=(0.,0.,0.)`) and instead accept positional arguments (without the argument name). You may run across this when trying to evaluate gradients so it's a good idea to keep in mind.\n",
    "\n",
    "We can take a look at our computed power and gradient information. "
   ]
  },
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   "id": "f0a786d2-88c7-406a-a6cd-956e6cfb904c",
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     "text": [
      "power = 0.552\n",
      "d_power/d_center = (array(0.00118849), array(1.05986359e-05), array(-0.00056509))\n",
      "d_power/d_size = (array(-0.01352494), array(0.1254442), array(-0.1322356))\n",
      "d_power/d_eps = -0.16138065820073802\n"
     ]
    }
   ],
   "source": [
    "print(f\"power = {power_value:.3f}\")\n",
    "print(f\"d_power/d_center = {dp_dcenter}\")\n",
    "print(f\"d_power/d_size = {dp_dsize}\")\n",
    "print(f\"d_power/d_eps = {dp_deps}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a20619d4-d14b-431f-b543-7f0f0bc2907a",
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    "From this, we can infer several things that fit our intuition, for example that:\n",
    "* the transmitted power should **decrease** if we increase the permittivity of our scatterer.\n",
    "* the transmitted power does not depend strongly on the position of the scatterer along the propagation direction.\n",
    "\n",
    "## Conclusion & Next Steps\n",
    "\n",
    "This gives the most basic introduction to the principles behind the adjoint plugin.\n",
    "\n",
    "In subsequent notebooks, we will show how to:\n",
    " * Check the gradients returned by this method against brute force computed gradients for accuracy.\n",
    " * Perform gradient-based optimization using the adjoint plugin."
   ]
  }
 ],
 "metadata": {
  "description": "This notebook introduces the basics of Jax, automatic differentiation, and the adjoint plugin in Tidy3D FDTD.",
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