diffphys-code-sol.ipynb

{
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   "source": [
    "# Reducing Numerical Errors with Deep Learning\n",
    "\n",
    "In this example we will target numerical errors that arise in the discretization of a continuous PDE $\\mathcal P^*$, i.e. when we formulate $\\mathcal P$. This approach will demonstrate that, despite the lack of closed-form descriptions, discretization errors often are functions with regular and repeating structures and, thus, can be learned by a neural network. Once the network is trained, it can be evaluated locally to improve the solution of a PDE-solver, i.e., to reduce its numerical error. The resulting method is a hybrid one: it will always run (a coarse) PDE solver, and then improve it at runtime with corrections inferred by an NN.\n",
    "\n",
    " \n",
    "Pretty much all numerical methods contain some form of iterative process: repeated updates over time for explicit solvers, or within a single update step for implicit solvers. \n",
    "An example for the second case could be found [here](https://github.com/tum-pbs/CG-Solver-in-the-Loop),\n",
    "but below we'll target the first case, i.e. iterations over time.\n",
    "[[run in colab]](https://colab.research.google.com/github/tum-pbs/pbdl-book/blob/main/diffphys-code-sol.ipynb)\n",
    "\n",
    "\n",
    "## Problem formulation\n",
    "\n",
    "In the context of reducing errors, it's crucial to have a _differentiable physics solver_, so that the learning process can take the reaction of the solver into account. This interaction is not possible with supervised learning or PINN training. Even small inference errors of a supervised NN accumulate over time, and lead to a data distribution that differs from the distribution of the pre-computed data. This distribution shift leads to sub-optimal results, or even cause blow-ups of the solver.\n",
    "\n",
    "In order to learn the error function, we'll consider two different discretizations of the same PDE $\\mathcal P^*$: \n",
    "a _reference_ version, which we assume to be accurate, with a discretized version \n",
    "$\\mathcal P_r$, and solutions $\\mathbf r \\in \\mathscr R$, where $\\mathscr R$ denotes the manifold of solutions of $\\mathcal P_r$.\n",
    "In parallel to this, we have a less accurate approximation of the same PDE, which we'll refer to as the _source_ version, as this will be the solver that our NN should later on interact with. Analogously,\n",
    "we have $\\mathcal P_s$ with solutions $\\mathbf s \\in \\mathscr S$.\n",
    "After training, we'll obtain a _hybrid_ solver that uses $\\mathcal P_s$ in conjunction with a trained network to obtain improved solutions, i.e., solutions that are closer to the ones produced by $\\mathcal P_r$.\n",
    "\n",
    "```{figure} resources/diffphys-sol-manifolds.jpeg\n",
    "---\n",
    "height: 150px\n",
    "name: diffphys-sol-manifolds\n",
    "---\n",
    "Visual overview of coarse and reference manifolds\n",
    "```\n"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {
    "id": "tayrJa7_ZzS_"
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   "source": [
    "\n",
    "Let's assume $\\mathcal{P}$ advances a solution by a time step $\\Delta t$, and let's denote $n$ consecutive steps by a superscript:\n",
    "$\n",
    "\\newcommand{\\pde}{\\mathcal{P}}\n",
    "\\newcommand{\\pdec}{\\pde_{s}}\n",
    "\\newcommand{\\vc}[1]{\\mathbf{s}_{#1}} \n",
    "\\newcommand{\\vr}[1]{\\mathbf{r}_{#1}} \n",
    "\\newcommand{\\vcN}{\\vs}          \n",
    "\\newcommand{\\project}{\\mathcal{T}}   \n",
    "\\pdec^n ( \\mathcal{T} \\vr{t} ) = \\pdec(\\pdec(\\cdots \\pdec( \\mathcal{T} \\vr{t}  )\\cdots)) .\n",
    "$ \n",
    "The corresponding state of the simulation is\n",
    "$\n",
    "\\mathbf{s}_{t+n} = \\mathcal{P}^n ( \\mathcal{T} \\mathbf{r}_{t} ) .\n",
    "$\n",
    "Here we assume a mapping operator $\\mathcal{T}$ exists that transfers a reference solution to the source manifold. This could, e.g., be a simple downsampling operation.\n",
    "Especially for longer sequences, i.e. larger $n$, the source state \n",
    "$\\newcommand{\\vc}[1]{\\mathbf{s}_{#1}} \\vc{t+n}$\n",
    "will deviate from a corresponding reference state\n",
    "$\\newcommand{\\vr}[1]{\\mathbf{r}_{#1}} \\vr{t+n}$. \n",
    "This is what we will address with an NN in the following.\n",
    "\n",
    "As before, we'll use an $L^2$-norm to quantify the deviations, i.e., \n",
    "an error function $\\newcommand{\\loss}{e} \n",
    "\\newcommand{\\corr}{\\mathcal{C}} \n",
    "\\newcommand{\\vc}[1]{\\mathbf{s}_{#1}} \n",
    "\\newcommand{\\vr}[1]{\\mathbf{r}_{#1}} \n",
    "\\loss (\\vc{t},\\mathcal{T} \\vr{t})=\\Vert\\vc{t}-\\mathcal{T} \\vr{t}\\Vert_2$. \n",
    "Our learning goal is to train at a correction operator \n",
    "$\\mathcal{C} ( \\mathbf{s} )$ such that \n",
    "a solution to which the correction is applied has a lower error than the original unmodified (source) \n",
    "solution: $\\newcommand{\\loss}{e} \n",
    "\\newcommand{\\corr}{\\mathcal{C}} \n",
    "\\newcommand{\\vr}[1]{\\mathbf{r}_{#1}} \n",
    "\\loss ( \\mathcal{P}_{s}( \\corr (\\mathcal{T} \\vr{t}) ) , \\mathcal{T} \\vr{t+1}) < \\loss ( \\mathcal{P}_{s}( \\mathcal{T} \\vr{t} ), \\mathcal{T} \\vr{t+1})$. \n",
    "\n",
    "The correction function \n",
    "$\\newcommand{\\vcN}{\\mathbf{s}} \\newcommand{\\corr}{\\mathcal{C}} \\corr (\\vcN | \\theta)$ \n",
    "is represented as a deep neural network with weights $\\theta$\n",
    "and receives the state $\\mathbf{s}$ to infer an additive correction field with the same dimension.\n",
    "To distinguish the original states $\\mathbf{s}$ from the corrected ones, we'll denote the latter with an added tilde $\\tilde{\\mathbf{s}}$.\n",
    "The overall learning goal now becomes\n",
    "\n",
    "$$\n",
    "\\newcommand{\\corr}{\\mathcal{C}}  \n",
    "\\newcommand{\\vr}[1]{\\mathbf{r}_{#1}} \n",
    "\\text{arg min}_\\theta \\big( ( \\mathcal{P}_{s} \\corr )^n ( \\mathcal{T} \\vr{t} ) - \\mathcal{T} \\vr{t+n} \\big)^2\n",
    "$$\n",
    "\n",
    "To simplify the notation, we've dropped the sum over different samples here (the $i$ from previous versions).\n",
    "A crucial bit that's easy to overlook in the equation above, is that the correction depends on the modified states, i.e.\n",
    "it is a function of\n",
    "$\\tilde{\\mathbf{s}}$, so we have \n",
    "$\\newcommand{\\vctN}{\\tilde{\\mathbf{s}}} \\newcommand{\\corr}{\\mathcal{C}} \\corr (\\vctN | \\theta)$.\n",
    "These states actually evolve over time when training. They don't exist beforehand.\n",
    "\n",
    "**TL;DR**:\n",
    "We'll train a network $\\mathcal{C}$ to reduce the numerical errors of a simulator with a more accurate reference. It's crucial to have the _source_ solver realized as a differential physics operator, such that it provides gradients for an improved training of $\\mathcal{C}$.\n",
    "\n",
    "<br>\n",
    "\n",
    "---\n"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {
    "id": "hPgwGkzYdIww"
   },
   "source": [
    "## Getting started with the implementation\n",
    "\n",
    "The following replicates an experiment from [Solver-in-the-loop: learning from differentiable physics to interact with iterative pde-solvers](https://ge.in.tum.de/publications/2020-um-solver-in-the-loop/) {cite}`holl2019pdecontrol`, further details can be found in section B.1 of the [appendix](https://arxiv.org/pdf/2007.00016.pdf) of the paper.\n",
    "\n",
    "First, let's download the prepared data set (for details on generation & loading cf. https://github.com/tum-pbs/Solver-in-the-Loop), and let's get the data handling out of the way, so that we can focus on the _interesting_ parts..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "JwZudtWauiGa",
    "outputId": "f284b19b-0a77-44de-befe-06e3218fe49d"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Downloading training data (73MB), this can take a moment the first time...\n",
      "Loaded data, 6 training sims\n"
     ]
    }
   ],
   "source": [
    "import os, sys, logging, argparse, pickle, glob, random, distutils.dir_util, urllib.request\n",
    "\n",
    "fname_train = 'sol-karman-2d-train.pickle'\n",
    "if not os.path.isfile(fname_train):\n",
    "  print(\"Downloading training data (73MB), this can take a moment the first time...\")\n",
    "  urllib.request.urlretrieve(\"https://physicsbaseddeeplearning.org/data/\"+fname_train, fname_train)\n",
    "\n",
    "with open(fname_train, 'rb') as f: data_preloaded = pickle.load(f)\n",
    "print(\"Loaded data, {} training sims\".format(len(data_preloaded)) )\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "RY1F4kdWPLNG"
   },
   "source": [
    "Also let's get installing / importing all the necessary libraries out of the way. The cell below by default contains a fix for the current colab version. If you're happy with your local install, make sure to disable the TensorFlow version change. And while we're at it, we also set the random seed - obviously, 42 is the ultimate choice here \ud83d\ude42"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "BGN4GqxkIueM",
    "outputId": "53dafe3f-e5b1-49d4-f9c0-8c2551e5f84f"
   },
   "outputs": [],
   "source": [
    "!yes|pip uninstall tensorflow\n",
    "!pip install --upgrade --quiet tensorflow==2.9 # for colab ignore msgs, should work despite these\n",
    "!pip install --upgrade --quiet phiflow==2.2\n",
    "from phi.tf.flow import *\n",
    "import tensorflow as tf\n",
    "from tensorflow import keras\n",
    "\n",
    "random.seed(42) \n",
    "np.random.seed(42)\n",
    "tf.random.set_seed(42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "OhnzPdoww11P"
   },
   "source": [
    "## Simulation setup\n",
    "\n",
    "Now we set up the _source_ simulation $\\mathcal{P}_{s}$. \n",
    "Note that we won't deal with \n",
    "$\\mathcal{P}_{r}$\n",
    "below: the downsampled reference data is contained in the training data set. It was generated with a four times finer discretization. Below we're focusing on the interaction of the source solver and the NN. \n",
    "\n",
    "This code block and the next ones will define lots of functions, that will be used later on for training.\n",
    "\n",
    "The `KarmanFlow` solver below simulates a relatively standard wake flow case with a spherical obstacle in a rectangular domain, and an explicit viscosity solve to obtain different Reynolds numbers. This is the geometry of the setup:\n",
    "\n",
    "```{figure} resources/diffphys-sol-domain.png\n",
    "---\n",
    "height: 200px\n",
    "name: diffphys-sol-domain\n",
    "---\n",
    "Domain setup for the wake flow case (sizes in the imlpementation are using an additional factor of 100).\n",
    "```\n",
    "\n",
    "The solver applies inflow boundary conditions for the y-velocity with a pre-multiplied mask (`vel_BcMask`), to set the y components at the bottom of the domain during the simulation step. This mask is created with the `HardGeometryMask` from phiflow, which initializes the spatially shifted entries for the components of a staggered grid correctly. The simulation step is quite straight forward: it computes contributions for viscosity, inflow, advection and finally makes the resulting motion divergence free via an implicit pressure solve:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "id": "6WNMcdWUw4EP"
   },
   "outputs": [],
   "source": [
    "class KarmanFlow():\n",
    "    def __init__(self, domain):\n",
    "        self.domain = domain\n",
    "\n",
    "        self.vel_BcMask = self.domain.staggered_grid(HardGeometryMask( Box(y=(None, 5), x=None) ) )\n",
    "    \n",
    "        self.inflow = self.domain.scalar_grid(Box(y=(25,75), x=(5,10)) ) # scale with domain if necessary!\n",
    "        self.obstacles = [Obstacle(Sphere(center=tensor([50, 50], channel(vector=\"y,x\")), radius=10))] \n",
    "        #\n",
    "\n",
    "    def step(self, density_in, velocity_in, re, res, buoyancy_factor=0, dt=1.0):\n",
    "        velocity = velocity_in\n",
    "        density = density_in\n",
    "\n",
    "        # viscosity\n",
    "        velocity = phi.flow.diffuse.explicit(field=velocity, diffusivity=1.0/re*dt*res*res, dt=dt)\n",
    "        \n",
    "        # inflow boundary conditions\n",
    "        velocity = velocity*(1.0 - self.vel_BcMask) + self.vel_BcMask * (1,0)\n",
    "\n",
    "        # advection \n",
    "        density = advect.semi_lagrangian(density+self.inflow, velocity, dt=dt)\n",
    "        velocity = advected_velocity = advect.semi_lagrangian(velocity, velocity, dt=dt)\n",
    "\n",
    "        # mass conservation (pressure solve)\n",
    "        pressure = None\n",
    "        velocity, pressure = fluid.make_incompressible(velocity, self.obstacles)\n",
    "        self.solve_info = { 'pressure': pressure, 'advected_velocity': advected_velocity }\n",
    "        \n",
    "        return [density, velocity]\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "RYFUGICgxk0K"
   },
   "source": [
    "## Network architecture\n",
    "\n",
    "We'll also define two alternative versions of a neural networks to represent \n",
    "$\\newcommand{\\vcN}{\\mathbf{s}} \\newcommand{\\corr}{\\mathcal{C}} \\corr$. In both cases we'll use fully convolutional networks, i.e. networks without any fully-connected layers. We'll use Keras within tensorflow to define the layers of the network (mostly via `Conv2D`), typically activated via ReLU and LeakyReLU functions, respectively.\n",
    "The inputs to the network are: \n",
    "- 2 fields with x,y velocity\n",
    "- the Reynolds number as constant channel.\n",
    "\n",
    "The output is: \n",
    "- a 2 component field containing the x,y velocity.\n",
    "\n",
    "First, let's define a small network consisting only of four convolutional layers with ReLU activations (we're also using keras here for simplicity). The input dimensions are determined from input tensor in the `inputs_dict` (it has three channels: u,v, and Re). Then we process the data via three conv layers with 32 features each, before reducing to 2 channels in the output. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "id": "qIrWYTy6xscA"
   },
   "outputs": [],
   "source": [
    "def network_small(inputs_dict):\n",
    "    l_input = keras.layers.Input(**inputs_dict)\n",
    "    block_0 = keras.layers.Conv2D(filters=32, kernel_size=5, padding='same')(l_input)\n",
    "    block_0 = keras.layers.LeakyReLU()(block_0)\n",
    "\n",
    "    l_conv1 = keras.layers.Conv2D(filters=32, kernel_size=5, padding='same')(block_0)\n",
    "    l_conv1 = keras.layers.LeakyReLU()(l_conv1)\n",
    "    l_conv2 = keras.layers.Conv2D(filters=32, kernel_size=5, padding='same')(l_conv1)\n",
    "    block_1 = keras.layers.LeakyReLU()(l_conv2)\n",
    "\n",
    "    l_output = keras.layers.Conv2D(filters=2,  kernel_size=5, padding='same')(block_1) # u, v\n",
    "    return keras.models.Model(inputs=l_input, outputs=l_output)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "YfHvdI7yxtdj"
   },
   "source": [
    "For flexibility (and larger-scale tests later on), let's also define a _proper_ ResNet with a few more layers. This architecture is the one from the original paper, and will give a fairly good performance (`network_small` above will train faster, but give a sub-optimal performance at inference time)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "TyfpA7Fbx0ro"
   },
   "outputs": [],
   "source": [
    "def network_medium(inputs_dict):\n",
    "    l_input = keras.layers.Input(**inputs_dict)\n",
    "    block_0 = keras.layers.Conv2D(filters=32, kernel_size=5, padding='same')(l_input)\n",
    "    block_0 = keras.layers.LeakyReLU()(block_0)\n",
    "\n",
    "    l_conv1 = keras.layers.Conv2D(filters=32, kernel_size=5, padding='same')(block_0)\n",
    "    l_conv1 = keras.layers.LeakyReLU()(l_conv1)\n",
    "    l_conv2 = keras.layers.Conv2D(filters=32, kernel_size=5, padding='same')(l_conv1)\n",
    "    l_skip1 = keras.layers.add([block_0, l_conv2])\n",
    "    block_1 = keras.layers.LeakyReLU()(l_skip1)\n",
    "\n",
    "    l_conv3 = keras.layers.Conv2D(filters=32, kernel_size=5, padding='same')(block_1)\n",
    "    l_conv3 = keras.layers.LeakyReLU()(l_conv3)\n",
    "    l_conv4 = keras.layers.Conv2D(filters=32, kernel_size=5, padding='same')(l_conv3)\n",
    "    l_skip2 = keras.layers.add([block_1, l_conv4])\n",
    "    block_2 = keras.layers.LeakyReLU()(l_skip2)\n",
    "\n",
    "    l_conv5 = keras.layers.Conv2D(filters=32, kernel_size=5, padding='same')(block_2)\n",
    "    l_conv5 = keras.layers.LeakyReLU()(l_conv5)\n",
    "    l_conv6 = keras.layers.Conv2D(filters=32, kernel_size=5, padding='same')(l_conv5)\n",
    "    l_skip3 = keras.layers.add([block_2, l_conv6])\n",
    "    block_3 = keras.layers.LeakyReLU()(l_skip3)\n",
    "\n",
    "    l_conv7 = keras.layers.Conv2D(filters=32, kernel_size=5, padding='same')(block_3)\n",
    "    l_conv7 = keras.layers.LeakyReLU()(l_conv7)\n",
    "    l_conv8 = keras.layers.Conv2D(filters=32, kernel_size=5, padding='same')(l_conv7)\n",
    "    l_skip4 = keras.layers.add([block_3, l_conv8])\n",
    "    block_4 = keras.layers.LeakyReLU()(l_skip4)\n",
    "\n",
    "    l_conv9 = keras.layers.Conv2D(filters=32, kernel_size=5, padding='same')(block_4)\n",
    "    l_conv9 = keras.layers.LeakyReLU()(l_conv9)\n",
    "    l_convA = keras.layers.Conv2D(filters=32, kernel_size=5, padding='same')(l_conv9)\n",
    "    l_skip5 = keras.layers.add([block_4, l_convA])\n",
    "    block_5 = keras.layers.LeakyReLU()(l_skip5)\n",
    "\n",
    "    l_output = keras.layers.Conv2D(filters=2,  kernel_size=5, padding='same')(block_5)\n",
    "    return keras.models.Model(inputs=l_input, outputs=l_output)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ew-MgPSlyLW-"
   },
   "source": [
    "Next, we're coming to two functions which are pretty important: they transform the simulation state into an input tensor for the network, and vice versa. Hence, they're the interface between _keras/tensorflow_ and _phiflow_.\n",
    "\n",
    "The `to_keras` function uses the two vector components via `vector['x']` and `vector['y']` to discard the outermost layer of the velocity field grids. This gives two tensors of equal size that are concatenated. \n",
    "It then adds a constant channel via `math.ones` that is multiplied by the desired Reynolds number in `ext_const_channel`. The resulting stack of grids is stacked along the `channels` dimensions, and represents an  input to the neural network. \n",
    "\n",
    "After network evaluation, we transform the output tensor back into a phiflow grid via the `to_phiflow` function. \n",
    "It converts the 2-component tensor that is returned by the network into a phiflow staggered grid object, so that it is compatible with the velocity field of the fluid simulation.\n",
    "(Note: these are two _centered_ grids with different sizes, so we leave the work to the `domain.staggered_grid` function, which also sets physical size and boundary conditions as given by the domain)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "id": "hhGFpTjGyRyg"
   },
   "outputs": [],
   "source": [
    "\n",
    "def to_keras(dens_vel_grid_array, ext_const_channel):\n",
    "    # align the sides the staggered velocity grid making its size the same as the centered grid\n",
    "    return math.stack(\n",
    "        [\n",
    "            math.pad( dens_vel_grid_array[1].vector['x'].values, {'x':(0,1)} , math.extrapolation.ZERO),\n",
    "            dens_vel_grid_array[1].vector['y'].y[:-1].values,         # v\n",
    "            math.ones(dens_vel_grid_array[0].shape)*ext_const_channel # Re\n",
    "        ],\n",
    "        math.channel('channels')\n",
    "    )\n",
    "\n",
    "def to_phiflow(tf_tensor, domain):\n",
    "    return domain.staggered_grid(\n",
    "        math.stack(\n",
    "            [\n",
    "                math.tensor(tf.pad(tf_tensor[..., 1], [(0,0), (0,1), (0,0)]), math.batch('batch'), math.spatial('y, x')), # v\n",
    "                math.tensor( tf_tensor[...,:-1, 0], math.batch('batch'), math.spatial('y, x')), # u \n",
    "            ], math.channel(vector=\"y,x\")\n",
    "        ) \n",
    "    )\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "VngMwN_9y00S"
   },
   "source": [
    "---\n",
    "\n",
    "## Data handling\n",
    "\n",
    "So far so good - we also need to take care of a few more mundane tasks, e.g., some data handling and randomization. Below we define a `Dataset` class that stores all \"ground truth\" reference data (already downsampled).\n",
    "\n",
    "We actually have a lot of data dimensions: multiple simulations, with many time steps, each with different fields. This makes the code below a bit more difficult to read.\n",
    "\n",
    "The data format for the numpy array `dataPreloaded`: is  `['sim_name', frame, field (dens & vel)]`, where each field has dimension `[batch-size, y-size, x-size, channels]` (this is the standard for a phiflow export)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "id": "tjywcdD2y20t"
   },
   "outputs": [],
   "source": [
    "class Dataset():\n",
    "    def __init__(self, data_preloaded, num_frames, num_sims=None, batch_size=1, is_testset=False):\n",
    "        self.epoch         = None\n",
    "        self.epochIdx      = 0\n",
    "        self.batch         = None\n",
    "        self.batchIdx      = 0\n",
    "        self.step          = None\n",
    "        self.stepIdx       = 0\n",
    "\n",
    "        self.dataPreloaded = data_preloaded\n",
    "        self.batchSize     = batch_size\n",
    "\n",
    "        self.numSims       = num_sims\n",
    "        self.numBatches    = num_sims//batch_size\n",
    "        self.numFrames     = num_frames\n",
    "        self.numSteps      = num_frames\n",
    "        \n",
    "        # initialize directory keys (using naming scheme from SoL codebase)\n",
    "        # constant additional per-sim channel: Reynolds numbers from data generation\n",
    "        # hard coded for training and test data here\n",
    "        if not is_testset:\n",
    "            self.dataSims = ['karman-fdt-hires-set/sim_%06d'%i for i in range(num_sims) ]\n",
    "            ReNrs = [160000.0, 320000.0, 640000.0,  1280000.0,  2560000.0,  5120000.0]\n",
    "            self.extConstChannelPerSim = { self.dataSims[i]:[ReNrs[i]] for i in range(num_sims) }\n",
    "        else:\n",
    "            self.dataSims = ['karman-fdt-hires-testset/sim_%06d'%i for i in range(num_sims) ]\n",
    "            ReNrs = [120000.0, 480000.0, 1920000.0, 7680000.0] \n",
    "            self.extConstChannelPerSim = { self.dataSims[i]:[ReNrs[i]] for i in range(num_sims) }\n",
    "\n",
    "        self.dataFrames = [ np.arange(num_frames) for _ in self.dataSims ]  \n",
    "\n",
    "        # debugging example, check shape of a single marker density field:\n",
    "        #print(format(self.dataPreloaded[self.dataSims[0]][0][0].shape )) \n",
    "        \n",
    "        # the data has the following shape ['sim', frame, field (dens/vel)] where each field is [batch-size, y-size, x-size, channels]\n",
    "        self.resolution = self.dataPreloaded[self.dataSims[0]][0][0].shape[1:3]  \n",
    "\n",
    "        # compute data statistics for normalization\n",
    "        self.dataStats = {\n",
    "            'std': (\n",
    "                np.std(np.concatenate([np.absolute(self.dataPreloaded[asim][i][0].reshape(-1)) for asim in self.dataSims for i in range(num_frames)], axis=-1)), # density\n",
    "                np.std(np.concatenate([np.absolute(self.dataPreloaded[asim][i][1].reshape(-1)) for asim in self.dataSims for i in range(num_frames)], axis=-1)), # x-velocity\n",
    "                np.std(np.concatenate([np.absolute(self.dataPreloaded[asim][i][2].reshape(-1)) for asim in self.dataSims for i in range(num_frames)], axis=-1)), # y-velocity\n",
    "            )\n",
    "        }\n",
    "        self.dataStats.update({\n",
    "            'ext.std': [ np.std([np.absolute(self.extConstChannelPerSim[asim][0]) for asim in self.dataSims]) ] # Reynolds Nr\n",
    "        })\n",
    "\n",
    "        \n",
    "        if not is_testset:\n",
    "            print(\"Data stats: \"+format(self.dataStats))\n",
    "\n",
    "\n",
    "    # re-shuffle data for next epoch\n",
    "    def newEpoch(self, exclude_tail=0, shuffle_data=True):\n",
    "        self.numSteps = self.numFrames - exclude_tail\n",
    "        simSteps = [ (asim, self.dataFrames[i][0:(len(self.dataFrames[i])-exclude_tail)]) for i,asim in enumerate(self.dataSims) ]\n",
    "        sim_step_pair = []\n",
    "        for i,_ in enumerate(simSteps):\n",
    "            sim_step_pair += [ (i, astep) for astep in simSteps[i][1] ]  # (sim_idx, step) ...\n",
    "\n",
    "        if shuffle_data: random.shuffle(sim_step_pair)\n",
    "        self.epoch = [ list(sim_step_pair[i*self.numSteps:(i+1)*self.numSteps]) for i in range(self.batchSize*self.numBatches) ]\n",
    "        self.epochIdx += 1\n",
    "        self.batchIdx = 0\n",
    "        self.stepIdx = 0\n",
    "\n",
    "    def nextBatch(self):  \n",
    "        self.batchIdx += self.batchSize\n",
    "        self.stepIdx = 0\n",
    "\n",
    "    def nextStep(self):\n",
    "        self.stepIdx += 1\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "twIMJ3V0N1FX"
   },
   "source": [
    "The `nextEpoch`, `nextBatch`, and `nextStep` functions will be called at training time to randomize the order of the training data.\n",
    "\n",
    "Now we need one more function that compiles the data for a mini batch to train with, called `getData` below. It returns batches of the desired size in terms of marker density, velocity, and Reynolds number.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "id": "Dfwd4TnqN1Tn"
   },
   "outputs": [],
   "source": [
    "# for class Dataset():\n",
    "def getData(self, consecutive_frames):\n",
    "    d_hi = [\n",
    "        np.concatenate([\n",
    "            self.dataPreloaded[\n",
    "                self.dataSims[self.epoch[self.batchIdx+i][self.stepIdx][0]] # sim_key\n",
    "            ][\n",
    "                self.epoch[self.batchIdx+i][self.stepIdx][1]+j # frames\n",
    "            ][0]\n",
    "            for i in range(self.batchSize)\n",
    "        ], axis=0) for j in range(consecutive_frames+1)\n",
    "    ]\n",
    "    u_hi = [\n",
    "        np.concatenate([\n",
    "            self.dataPreloaded[\n",
    "                self.dataSims[self.epoch[self.batchIdx+i][self.stepIdx][0]] # sim_key\n",
    "            ][\n",
    "                self.epoch[self.batchIdx+i][self.stepIdx][1]+j # frames\n",
    "            ][1]\n",
    "            for i in range(self.batchSize)\n",
    "        ], axis=0) for j in range(consecutive_frames+1)\n",
    "    ]\n",
    "    v_hi = [\n",
    "        np.concatenate([\n",
    "            self.dataPreloaded[\n",
    "                self.dataSims[self.epoch[self.batchIdx+i][self.stepIdx][0]] # sim_key\n",
    "            ][\n",
    "                self.epoch[self.batchIdx+i][self.stepIdx][1]+j # frames\n",
    "            ][2]\n",
    "            for i in range(self.batchSize)\n",
    "        ], axis=0) for j in range(consecutive_frames+1)\n",
    "    ]\n",
    "    ext = [\n",
    "        self.extConstChannelPerSim[\n",
    "            self.dataSims[self.epoch[self.batchIdx+i][self.stepIdx][0]]\n",
    "        ][0] for i in range(self.batchSize)\n",
    "    ]\n",
    "    return [d_hi, u_hi, v_hi, ext]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "bIWnyPYlz8q7"
   },
   "source": [
    "Note that the `density` here denotes a passively advected marker field, and not the density of the fluid. Below we'll be focusing on the velocity only, the marker density is tracked purely for visualization purposes.\n",
    "\n",
    "After all the definitions we can finally run some code. We define the dataset object with the downloaded data from the first cell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "59EBdEdj0QR2",
    "outputId": "c6f13916-2764-45dc-89f1-22890cb2662b"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data stats: {'std': (2.6542656, 0.23155601, 0.3066732), 'ext.std': [1732512.6262166172]}\n"
     ]
    }
   ],
   "source": [
    "nsims = 6\n",
    "batch_size = 3\n",
    "simsteps = 500\n",
    "\n",
    "dataset = Dataset( data_preloaded=data_preloaded, num_frames=simsteps, num_sims=nsims, batch_size=batch_size )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "0N92RooWPzeA"
   },
   "source": [
    "Additionally, we've defined several global variables to control the training and the simulation in the next code cells.\n",
    "\n",
    "The most important and interesting one is `msteps`. It defines the number of simulation steps that are unrolled at each training iteration. This directly influences the runtime of each training step, as we first have to simulate all steps forward, and then backpropagate the gradient through all `msteps` simulation steps interleaved with the NN evaluations. However, this is where we'll receive important feedback in terms of gradients how the inferred corrections actually influence a running simulation. Hence, larger `msteps` are typically better.\n",
    "\n",
    "In addition we define the resolution of the simulation in `source_res`, and allocate the fluid solver object called `simulator`. In order to create grids, it requires access to a `Domain` object, which mostly exists for convenience purposes: it stores resolution, physical size in `bounds`, and boundary conditions of the domain. This information needs to be passed to every grid, and hence it's convenient to have it in one place in the form of the `Domain`. For the setup described above, we need different boundary conditions along x and y: closed walls, and free flow in and out of the domain, respecitvely.\n",
    "\n",
    "We also instantiate the actual NN `network` in the next cell. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "EjgkdCzKP2Ip",
    "outputId": "9e95aa79-6124-4e30-baf1-28bc37801b0f"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"model\"\n",
      "_________________________________________________________________\n",
      " Layer (type)                Output Shape              Param #   \n",
      "=================================================================\n",
      " input_1 (InputLayer)        [(None, 64, 32, 3)]       0         \n",
      "                                                                 \n",
      " conv2d (Conv2D)             (None, 64, 32, 32)        2432      \n",
      "                                                                 \n",
      " leaky_re_lu (LeakyReLU)     (None, 64, 32, 32)        0         \n",
      "                                                                 \n",
      " conv2d_1 (Conv2D)           (None, 64, 32, 32)        25632     \n",
      "                                                                 \n",
      " leaky_re_lu_1 (LeakyReLU)   (None, 64, 32, 32)        0         \n",
      "                                                                 \n",
      " conv2d_2 (Conv2D)           (None, 64, 32, 32)        25632     \n",
      "                                                                 \n",
      " leaky_re_lu_2 (LeakyReLU)   (None, 64, 32, 32)        0         \n",
      "                                                                 \n",
      " conv2d_3 (Conv2D)           (None, 64, 32, 2)         1602      \n",
      "                                                                 \n",
      "=================================================================\n",
      "Total params: 55,298\n",
      "Trainable params: 55,298\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "# one of the most crucial parameters: how many simulation steps to look into the future while training\n",
    "msteps = 4\n",
    "\n",
    "# # this is the actual resolution in terms of cells\n",
    "source_res = list(dataset.resolution)\n",
    "# # this is a virtual size, in terms of abstract units for the bounding box of the domain (it's important for conversions or when rescaling to physical units)\n",
    "simulation_length = 100.\n",
    "\n",
    "# for readability\n",
    "from phi.physics._boundaries import Domain, OPEN, STICKY as CLOSED\n",
    "\n",
    "boundary_conditions = {\n",
    "    'y':(phi.physics._boundaries.OPEN,  phi.physics._boundaries.OPEN) ,\n",
    "    'x':(phi.physics._boundaries.STICKY,phi.physics._boundaries.STICKY) \n",
    "}\n",
    "\n",
    "domain = phi.physics._boundaries.Domain(y=source_res[0], x=source_res[1], boundaries=boundary_conditions, bounds=Box(y=2*simulation_length, x=simulation_length))\n",
    "simulator = KarmanFlow(domain=domain)\n",
    "\n",
    "network = network_small(dict(shape=(source_res[0],source_res[1], 3)))\n",
    "network.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "AbpNPzplQZMF"
   },
   "source": [
    "## Interleaving simulation and NN\n",
    "\n",
    "Now comes the **most crucial** step in the whole setup: we define a function that encapsulates the chain of simulation steps and network evaluations in each training step. After all the work defining helper functions, it's actually pretty simple: we create a gradient tape via `tf.GradientTape()` such that we can backpropagate later on. We then loop over `msteps`, call the simulator via `simulator.step` for an input state, and afterwards evaluate the correction via `network(to_keras(...))`. The NN correction is then added to the last simulation state in the `prediction` list (we're actually simply overwriting the last simulated velocity `prediction[-1][1]` with `prediction[-1][1] + correction[-1]`.\n",
    "\n",
    "One other important thing that's happening here is normalization: the inputs to the network are divided by the standard deviations in `dataset.dataStats`. After evaluating the `network`, we only have a velocity left, so we simply multiply it by the standard deviation of the velocity again (via `* dataset.dataStats['std'][1]` and `[2]`).\n",
    "\n",
    "The `training_step` function also directly evaluates and returns the loss. Here, we simply use an $L^2$ loss over the whole sequence, i.e. the iteration over `msteps`. This is requiring a few lines of code because we separately loop over 'x' and 'y' components, in order to normalize and compare to the ground truth values from the training data set.\n",
    "\n",
    "The \"learning\" happens in the last two lines via `tape.gradient()` and `opt.apply_gradients()`, which then contain the aggregated information about how to change the NN weights to nudge the simulation closer to the reference for the full chain of simulation steps."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "id": "D5NeMcLGQaxh",
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "def training_step(dens_gt, vel_gt, Re, i_step):\n",
    "    with tf.GradientTape() as tape:\n",
    "        prediction, correction = [ [dens_gt[0],vel_gt[0]] ], [0] # predicted states with correction, inferred velocity corrections\n",
    "\n",
    "        for i in range(msteps):\n",
    "            prediction += [\n",
    "                simulator.step(\n",
    "                    density_in=prediction[-1][0],\n",
    "                    velocity_in=prediction[-1][1],\n",
    "                    re=Re, res=source_res[1],\n",
    "                )\n",
    "            ]       # prediction: [[density1, velocity1], [density2, velocity2], ...]\n",
    "\n",
    "            model_input = to_keras(prediction[-1], Re)\n",
    "            model_input /= math.tensor([dataset.dataStats['std'][1], dataset.dataStats['std'][2], dataset.dataStats['ext.std'][0]], channel('channels')) # [u, v, Re]\n",
    "            model_out = network(model_input.native(['batch', 'y', 'x', 'channels']), training=True)\n",
    "            model_out *= [dataset.dataStats['std'][1], dataset.dataStats['std'][2]] # [u, v]\n",
    "            correction += [ to_phiflow(model_out, domain) ]                         # [velocity_correction1, velocity_correction2, ...]\n",
    "\n",
    "            prediction[-1][1] = prediction[-1][1] + correction[-1]\n",
    " \n",
    "        # evaluate loss\n",
    "        loss_steps_x = [\n",
    "            tf.nn.l2_loss(\n",
    "                (\n",
    "                    vel_gt[i].vector['x'].values.native(('batch', 'y', 'x'))\n",
    "                    - prediction[i][1].vector['x'].values.native(('batch', 'y', 'x'))\n",
    "                )/dataset.dataStats['std'][1]\n",
    "            )\n",
    "            for i in range(1,msteps+1)\n",
    "        ]\n",
    "        loss_steps_x_sum = tf.math.reduce_sum(loss_steps_x)\n",
    "\n",
    "        loss_steps_y = [\n",
    "            tf.nn.l2_loss(\n",
    "                (\n",
    "                    vel_gt[i].vector['y'].values.native(('batch', 'y', 'x'))\n",
    "                    - prediction[i][1].vector['y'].values.native(('batch', 'y', 'x'))\n",
    "                )/dataset.dataStats['std'][2]\n",
    "            )\n",
    "            for i in range(1,msteps+1)\n",
    "        ]\n",
    "        loss_steps_y_sum = tf.math.reduce_sum(loss_steps_y)\n",
    "\n",
    "        loss = (loss_steps_x_sum + loss_steps_y_sum)/msteps\n",
    "\n",
    "        gradients = tape.gradient(loss, network.trainable_variables)\n",
    "        opt.apply_gradients(zip(gradients, network.trainable_variables))\n",
    "\n",
    "        return math.tensor(loss)    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "c4yLlDM3QfUR"
   },
   "source": [
    "Once defined, we prepare this function for executing the training step by calling phiflow's `math.jit_compile()` function. It automatically maps to the correct pre-compilation step of the chosen backend. E.g., for TF this internally creates a computational graph, and optimizes the chain of operations. For JAX, it can even compile optimized GPU code (if JAX is set up correctly). Thus, using the jit compilation can make a huge difference in terms of runtime."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "id": "K2JcO3-QQgC9"
   },
   "outputs": [],
   "source": [
    "training_step_jit = math.jit_compile(training_step)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "E6Vly1_0QhZ1"
   },
   "source": [
    "## Training\n",
    "\n",
    "For the training, we use a standard Adam optimizer, and run 5 epochs by default. This is a fairly low number to keep the runtime low. If you have the resources, 10 or 15 epochs will yield more accurate results. For even longer training runs and larger networks, it would also be beneficial to decrease the learning rate over the course of the epochs, but for simplicity, we'll keep `LR` constant here.\n",
    "\n",
    "Optionally, this is also the right point to load a network state to resume training."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "id": "PuljFamYQksW"
   },
   "outputs": [],
   "source": [
    "LR = 1e-4\n",
    "EPOCHS = 5\n",
    "\n",
    "opt = tf.keras.optimizers.Adam(learning_rate=LR) \n",
    "\n",
    "# optional, load existing network...\n",
    "# set to epoch nr. to load existing network from there\n",
    "resume = 0\n",
    "if resume>0: \n",
    "    ld_network = keras.models.load_model('./nn_epoch{:04d}.h5'.format(resume)) \n",
    "    #ld_network = keras.models.load_model('./nn_final.h5') # or the last one\n",
    "    network.set_weights(ld_network.get_weights())\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "lrALctV1RWBO"
   },
   "source": [
    "Finally, we can start training the NN! This is very straight forward now, we simply loop over the desired number of iterations, get a batch each time via `getData`, feed it into the source simulation input `source_in`, and compare it in the loss with the `reference` data for the batch.\n",
    "\n",
    "The setup above will automatically take care that the differentiable physics solver used here provides the right gradient information, and provides it to the tensorflow network. Be warned: due to the complexity of the setup, this training run can take a while... (If you have a saved `nn_final.h5` network from a previous run, you can potentially skip this block and load the previously trained model instead via the cell above.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "m3Nd8YyHRVFQ",
    "outputId": "486715ab-73dd-4301-b5f3-db34b1d9c3c4",
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 001/005, batch 001/002, step 0001/0496: loss=\u001b[94m2565.1914\u001b[0m\n",
      "epoch 001/005, batch 001/002, step 0002/0496: loss=\u001b[94m1434.6736\u001b[0m\n",
      "epoch 001/005, batch 001/002, step 0003/0496: loss=\u001b[94m724.7997\u001b[0m\n",
      "epoch 001/005, batch 001/002, step 0129/0496: loss=\u001b[94m40.198242\u001b[0m\n",
      "epoch 001/005, batch 001/002, step 0257/0496: loss=\u001b[94m28.450535\u001b[0m\n",
      "epoch 001/005, batch 001/002, step 0385/0496: loss=\u001b[94m27.100056\u001b[0m\n",
      "epoch 002/005, batch 001/002, step 0401/0496: loss=\u001b[94m8.376183\u001b[0m\n",
      "epoch 003/005, batch 001/002, step 0401/0496: loss=\u001b[94m4.7433133\u001b[0m\n",
      "epoch 004/005, batch 001/002, step 0401/0496: loss=\u001b[94m4.522671\u001b[0m\n",
      "epoch 005/005, batch 001/002, step 0401/0496: loss=\u001b[94m2.0179803\u001b[0m\n",
      "Training done, saved NN\n"
     ]
    }
   ],
   "source": [
    "steps = 0\n",
    "for j in range(EPOCHS):  # training\n",
    "    dataset.newEpoch(exclude_tail=msteps)\n",
    "    if j<resume:\n",
    "        print('resume: skipping {} epoch'.format(j+1))\n",
    "        steps += dataset.numSteps*dataset.numBatches\n",
    "        continue\n",
    "\n",
    "    for ib in range(dataset.numBatches):   \n",
    "        for i in range(dataset.numSteps): \n",
    "\n",
    "            # batch: [[dens0, dens1, ...], [x-velo0, x-velo1, ...], [y-velo0, y-velo1, ...], [ReynoldsNr(s)]]            \n",
    "            batch = getData(dataset, consecutive_frames=msteps)\n",
    "            \n",
    "            dens_gt = [   # [density0:CenteredGrid, density1, ...]\n",
    "                domain.scalar_grid(\n",
    "                    math.tensor(batch[0][k], math.batch('batch'), math.spatial('y, x')) \n",
    "                ) for k in range(msteps+1)\n",
    "            ]\n",
    "\n",
    "            vel_gt = [   # [velocity0:StaggeredGrid, velocity1, ...]\n",
    "                domain.staggered_grid(\n",
    "                    math.stack(\n",
    "                        [\n",
    "                            math.tensor(batch[2][k], math.batch('batch'), math.spatial('y, x')),\n",
    "                            math.tensor(batch[1][k], math.batch('batch'), math.spatial('y, x')),\n",
    "                        ], math.channel(vector=\"y,x\")\n",
    "                    ) \n",
    "                ) for k in range(msteps+1)\n",
    "            ]\n",
    "            re_nr = math.tensor(batch[3], math.batch('batch'))\n",
    "\n",
    "            loss = training_step_jit(dens_gt, vel_gt, re_nr, math.tensor(steps)) \n",
    "            \n",
    "            steps += 1\n",
    "            if (j==0 and ib==0 and i<3) or (j==0 and ib==0 and i%128==0) or (j>0 and ib==0 and i==400): # reduce output \n",
    "              print('epoch {:03d}/{:03d}, batch {:03d}/{:03d}, step {:04d}/{:04d}: loss={}'.format( j+1, EPOCHS, ib+1, dataset.numBatches, i+1, dataset.numSteps, loss ))\n",
    "            \n",
    "            dataset.nextStep()\n",
    "\n",
    "        dataset.nextBatch()\n",
    "\n",
    "    if j%10==9: network.save('./nn_epoch{:04d}.h5'.format(j+1))\n",
    "\n",
    "# all done! save final version\n",
    "network.save('./nn_final.h5'); print(\"Training done, saved NN\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "swG7GeDpWT_Z"
   },
   "source": [
    "The loss should go down from above 1000 initially to below 10. This is a good sign, but of course it's even more important to see how the NN-solver combination fares on new inputs. With this training approach we've realized a hybrid solver, consisting of a regular _source_ simulator, and a network that was trained to specifically interact with this simulator for a chosen domain of simulation cases.\n",
    "\n",
    "Let's see how well this works by applying it to a set of test data inputs with new Reynolds numbers that were not part of the training data.\n",
    "\n",
    "To keep things somewhat simple, we won't aim for a high-performance version of our hybrid solver. For performance, please check out the external code base: the network trained here should be directly useable in [this apply script](https://github.com/tum-pbs/Solver-in-the-Loop/blob/master/karman-2d/karman_apply.py).\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "0c38ne0UdIxV"
   },
   "source": [
    "## Evaluation \n",
    "\n",
    "In order to evaluate the performance of our DL-powered solver, we essentially only need to repeat the inner loop of each training iteration for more steps. While we were limited to `msteps` evaluations at training time, we can now run our solver for arbitrary lengths. This is a good test for how well our solver has learned to keep the data within the desired distribution, and represents a generalization test for longer rollouts.\n",
    "\n",
    "We reuse the solver code from above, but in the following, we will consider two simulated versions: for comparison, we'll run one reference simulation in the _source_ space (i.e., without any modifications). This version receives the regular outputs of each evaluation of the simulator, and ignores the learned correction (stored in `steps_source` below). The second version, repeatedly computes the source solver plus the learned correction, and advances this state in the solver (`steps_hybrid`).\n",
    "\n",
    "We also need a set of new data. Below, we'll download a new set of Reynolds numbers (in between the ones used for training), on which we will later on run the unmodified simulator and the DL-powered one.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "id": "RumKebW_05xp"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Downloading test data (38MB), this can take a moment the first time...\n",
      "Loaded test data, 4 training sims\n"
     ]
    }
   ],
   "source": [
    "fname_test = 'sol-karman-2d-test.pickle'\n",
    "if not os.path.isfile(fname_test):\n",
    "  print(\"Downloading test data (38MB), this can take a moment the first time...\")\n",
    "  urllib.request.urlretrieve(\"https://physicsbaseddeeplearning.org/data/\"+fname_test, fname_test)\n",
    "\n",
    "with open(fname_test, 'rb') as f: data_test_preloaded = pickle.load(f)\n",
    "print(\"Loaded test data, {} training sims\".format(len(data_test_preloaded)) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "rZ9h-gRddIxb"
   },
   "source": [
    "Next we create a new dataset object `dataset_test` that organizes the data. We're simply using the first batch of the unshuffled dataset, though.\n",
    "\n",
    "A subtle but important point: we still have to use the normalization from the original training data set: `dataset.dataStats['std']` values. The test data set has it's own mean and standard deviation, and so the trained NN never saw this data before. The NN was trained with the data in `dataset` above, and hence we have to use the constants from there for normalization to make sure the network receives values that it can relate to the data it was trained with."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "id": "9OPruTGMdIxe"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reynolds numbers in test data set: \u001b[94m(120000.000, 480000.000, 1920000.000, 7680000.000)\u001b[0m along \u001b[92mbatch\u1d47\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "dataset_test = Dataset( data_preloaded=data_test_preloaded, is_testset=True, num_frames=simsteps, num_sims=4, batch_size=4 )\n",
    "\n",
    "# we only need 1 batch with t=0 states to initialize the test simulations with\n",
    "dataset_test.newEpoch(shuffle_data=False)\n",
    "batch = getData(dataset_test, consecutive_frames=0) \n",
    "\n",
    "re_nr_test = math.tensor(batch[3], math.batch('batch')) # Reynolds numbers\n",
    "print(\"Reynolds numbers in test data set: \"+format(re_nr_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "sMqRPg2pdIxh"
   },
   "source": [
    "Next we construct a `math.tensor` as initial state for the centered marker fields, and a staggered grid from the next two indices of the test set batch. Similar to `to_phiflow` above, we use `phi.math.stack()` to combine two fields of appropriate size as a staggered grid."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "id": "xK1MEaPqdIxi"
   },
   "outputs": [],
   "source": [
    "source_dens_initial = math.tensor( batch[0][0], math.batch('batch'), math.spatial('y, x'))\n",
    "\n",
    "source_vel_initial = domain.staggered_grid(phi.math.stack([\n",
    "    math.tensor(batch[2][0], math.batch('batch'),math.spatial('y, x')),\n",
    "    math.tensor(batch[1][0], math.batch('batch'),math.spatial('y, x'))], channel(vector=\"y,x\")) )\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "KhGVceo6dIxl"
   },
   "source": [
    "Now we first run the _source_ simulation for 120 steps as baseline:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "id": "nbTTl15kdIxl"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Source simulation steps 101\n"
     ]
    }
   ],
   "source": [
    "source_dens_test, source_vel_test = source_dens_initial, source_vel_initial\n",
    "steps_source = [[source_dens_test,source_vel_test]]\n",
    "STEPS=100\n",
    "\n",
    "# note - math.jit_compile() not useful for numpy solve... hence not necessary here\n",
    "for i in range(STEPS):\n",
    "    [source_dens_test,source_vel_test] = simulator.step(\n",
    "        density_in=source_dens_test,\n",
    "        velocity_in=source_vel_test,\n",
    "        re=re_nr_test,\n",
    "        res=source_res[1],\n",
    "    )\n",
    "    steps_source.append( [source_dens_test,source_vel_test] )\n",
    "\n",
    "print(\"Source simulation steps \"+format(len(steps_source)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "vQV0qV5pdIxm"
   },
   "source": [
    "Next, we compute the corresponding states of our learned hybrid solver. Here, we closely follow the training code, however, now without any gradient tapes or loss computations. We only evaluate the NN in a forward pass for each simulated state to compute a correction field:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "id": "fH5tFfh9dIxn"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Steps with hybrid solver 101\n"
     ]
    }
   ],
   "source": [
    "source_dens_test, source_vel_test = source_dens_initial, source_vel_initial\n",
    "steps_hybrid = [[source_dens_test,source_vel_test]]\n",
    "        \n",
    "for i in range(STEPS):\n",
    "    [source_dens_test,source_vel_test] = simulator.step(\n",
    "        density_in=source_dens_test,\n",
    "        velocity_in=source_vel_test,\n",
    "        re=math.tensor(re_nr_test),\n",
    "        res=source_res[1],\n",
    "    )\n",
    "    model_input = to_keras([source_dens_test,source_vel_test], re_nr_test )\n",
    "    model_input /= math.tensor([dataset.dataStats['std'][1], dataset.dataStats['std'][2], dataset.dataStats['ext.std'][0]], channel('channels')) # [u, v, Re]\n",
    "    model_out = network(model_input.native(['batch', 'y', 'x', 'channels']), training=False)\n",
    "    model_out *= [dataset.dataStats['std'][1], dataset.dataStats['std'][2]] # [u, v]\n",
    "    correction =  to_phiflow(model_out, domain) \n",
    "    source_vel_test = source_vel_test + correction\n",
    "\n",
    "    steps_hybrid.append( [source_dens_test, source_vel_test] )\n",
    "    \n",
    "print(\"Steps with hybrid solver \"+format(len(steps_hybrid)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "tnHYeOfldIxp"
   },
   "source": [
    "Given the stored states, we quantify the improvements that the NN yields, and visualize the results. \n",
    "\n",
    "In the following cells, the index `b` chooses one of the four test simulations (by default index 0, the lowest Re outside the training data range), and computes the accumulated mean absolute error (MAE) over all time steps.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "id": "bU-PwcCCdIxq"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MAE for source: 0.12054027616977692 , and hybrid: 0.04435234144330025\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pylab\n",
    "b = 0 # batch index for the following comparisons\n",
    "\n",
    "errors_source, errors_pred = [], []\n",
    "for index in range(STEPS):\n",
    "  vx_ref = dataset_test.dataPreloaded[ dataset_test.dataSims[b] ][ index ][1][0,...]\n",
    "  vy_ref = dataset_test.dataPreloaded[ dataset_test.dataSims[b] ][ index ][2][0,...]\n",
    "  vxs = vx_ref - steps_source[index][1].values.vector[1].numpy('batch,y,x')[b,...]\n",
    "  vxh = vx_ref - steps_hybrid[index][1].values.vector[1].numpy('batch,y,x')[b,...]\n",
    "  vys = vy_ref - steps_source[index][1].values.vector[0].numpy('batch,y,x')[b,...] \n",
    "  vyh = vy_ref - steps_hybrid[index][1].values.vector[0].numpy('batch,y,x')[b,...] \n",
    "  errors_source.append(np.mean(np.abs(vxs)) + np.mean(np.abs(vys))) \n",
    "  errors_pred.append(np.mean(np.abs(vxh)) + np.mean(np.abs(vyh)))\n",
    "\n",
    "fig = pylab.figure().gca()\n",
    "pltx = np.linspace(0,STEPS-1,STEPS)\n",
    "fig.plot(pltx, errors_source, lw=2, color='mediumblue', label='Source')  \n",
    "fig.plot(pltx, errors_pred,   lw=2, color='green', label='Hybrid')\n",
    "pylab.xlabel('Time step'); pylab.ylabel('Error'); fig.legend()\n",
    "\n",
    "print(\"MAE for source: \"+format(np.mean(errors_source)) +\" , and hybrid: \"+format(np.mean(errors_pred)) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "aOQP6iCBdIxs"
   },
   "source": [
    "Due to the complexity of the training, the performance varies but typically the overall MAE is ca. $2.5\\times$ larger for the regular simulation compared to the hybrid simulator. The graph above also shows this behavior over time.\n",
    "The gap is usually even larger for other Reynolds numbers within the training data range (try other values for `b` above). \n",
    "\n",
    "Let's also visualize the differences of the two outputs by plotting the y component of the velocities over time. The two following code cells show six velocity snapshots for the batch index `b` in intervals of 20 time steps."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "id": "_3f8uhIIdIxs"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x360 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "c = 0          # channel selector, x=1 or y=0 \n",
    "interval = 20  # time interval\n",
    "IMGS = STEPS//20+1\n",
    "\n",
    "fig, axes = pylab.subplots(1, IMGS, figsize=(16, 5))    \n",
    "for i in range(0,IMGS):\n",
    "  v = steps_source[i*interval][1].values.vector[c].numpy('batch,y,x')[b,...]\n",
    "  axes[i].imshow( v , origin='lower', cmap='magma')\n",
    "  axes[i].set_title(f\" Source simulation t={i*interval} \")\n",
    "\n",
    "pylab.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "id": "v2d2WTGedIxt"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x360 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = pylab.subplots(1, IMGS, figsize=(16, 5))\n",
    "for i in range(0,IMGS):\n",
    "  v = steps_hybrid[i*interval][1].values.vector[c].numpy('batch,y,x')[b,...]\n",
    "  axes[i].imshow( v , origin='lower', cmap='magma')\n",
    "  axes[i].set_title(f\" Hybrid solver t={i*interval} \")\n",
    "pylab.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ivS0SUiYdIxt"
   },
   "source": [
    "They both start out with the same initial state at $t=0$ (the downsampled solution from the reference solution manifold), and at $t=20$ the solutions still share similarities. Over time, the source version strongly diffuses the structures in the flow and looses momentum. The flow behind the obstacles becomes straight, and lacks clear vortices. \n",
    "\n",
    "The version produced by the hybrid solver does much better. It preserves the vortex shedding even after more than one hundred updates. Note that both outputs were produced by the same underlying solver. The second version just profits from the learned corrector which manages to revert the numerical errors of the source solver, including its overly strong dissipation. \n",
    "\n",
    "We also visually compare how the NN does w.r.t. reference data. The next cell plots one time step of the three versions: the reference data after 50 steps, and the re-simulated version of the source and our hybrid solver, together with a per-cell error of the two:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "id": "23yyfljqdIxu"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "index = STEPS//2 # time step index\n",
    "vx_ref = dataset_test.dataPreloaded[ dataset_test.dataSims[b] ][ index ][1][0,...]\n",
    "vx_src = steps_source[index][1].values.vector[1].numpy('batch,y,x')[b,...]\n",
    "vx_hyb = steps_hybrid[index][1].values.vector[1].numpy('batch,y,x')[b,...]\n",
    "\n",
    "fig, axes = pylab.subplots(1, 4, figsize=(14, 5))\n",
    "\n",
    "axes[0].imshow( vx_ref , origin='lower', cmap='magma')\n",
    "axes[0].set_title(f\" Reference \")\n",
    "\n",
    "axes[1].imshow( vx_src , origin='lower', cmap='magma')\n",
    "axes[1].set_title(f\" Source \")\n",
    "\n",
    "axes[2].imshow( vx_hyb , origin='lower', cmap='magma')\n",
    "axes[2].set_title(f\" Learned \")\n",
    "\n",
    "# show error side by side\n",
    "err_source = vx_ref - vx_src \n",
    "err_hybrid = vx_ref - vx_hyb \n",
    "v = np.concatenate([err_source,err_hybrid], axis=1)\n",
    "axes[3].imshow( v , origin='lower', cmap='cividis')\n",
    "axes[3].set_title(f\" Errors: Source & Learned\")\n",
    "\n",
    "pylab.tight_layout()\n"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {
    "id": "BZByQsAydIxv"
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   "source": [
    "This shows very clearly how the pure source simulation in the middle deviates from the reference on the left. The learned version stays much closer to the reference solution. \n",
    "\n",
    "The two per-cell error images on the right also illustrate this: the source version has much larger errors (i.e. brighter colors) that show how it systematically underestimates the vortices that should form. The error for the learned version is much more evenly distributed and significantly smaller in magnitude.\n"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {
    "id": "UQTY8m6LdIxv"
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   "source": [
    "This concludes our evaluation. Note that the improved behavior of the hybrid solver can be difficult to reliably measure with simple vector norms such as an MAE or $L^2$ norm. To improve this, we'd need to employ other, domain-specific metrics. In this case, metrics for fluids based on vorticity and turbulence properties of the flow would be applicable. However, in this text, we instead want to focus on DL-related topics and target another inverse problem with differentiable physics solvers in the next chapter."
   ]
  },
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   "cell_type": "markdown",
   "metadata": {
    "id": "Dl3vzF_XdIxv"
   },
   "source": [
    "## Next steps\n",
    "\n",
    "* Modify the training to further reduce the training error. With the _medium_ network you should be able to get the loss down to around 1.\n",
    "\n",
    "* Turn off the differentiable physics training (by setting `msteps=1`), and compare it with the DP version.\n",
    "\n",
    "* Likewise, train a network with a larger `msteps` setting, e.g., 8 or 16. Note that due to the recurrent nature of the training, you'll probably have to load a pre-trained state to stabilize the first iterations.\n",
    "\n",
    "* Use the external github code to generate new test data, and run your trained NN on these cases. You'll see that a reduced training error not always directly correlates with an improved test performance.\n",
    "\n"
   ]
  }
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