notebooks/Control Burgers.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Learning to Control Burgers Equation with Differentiable Physics\n",
    "This notebook will walk you through data generation, supervised network initialization and end-to-end training using our differentiable PDE solver, [Φ<sub>Flow</sub>](https://github.com/tum-pbs/PhiFlow).\n",
    "\n",
    "The code below replicates experiment 1 from the ICLR 2020 paper [Learning to Control PDEs with Differentiable Physics](https://ge.in.tum.de/publications/2020-iclr-holl/). The original experiment was performed on an older version of the solver, the code for which can be found under `/legacy`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys; sys.path.append('../PhiFlow'); sys.path.append('../src')\n",
    "from control.pde.burgers import GaussianClash, GaussianForce\n",
    "import burgers_plots as bplt\n",
    "import matplotlib.pyplot as plt\n",
    "from phi.flow import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Generation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "domain = Domain([128], box=box[0:1])  # 1D Grid resolution and physical size\n",
    "viscosity = 0.003  # Viscosity constant for Burgers equation\n",
    "step_count = 32  # how many solver steps to perform\n",
    "dt = 0.03  # Time increment per solver step"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's have a look at an example Burgers simulation with Gaussian forcing. The classes `BurgersVelocity` and `Burgers` are part of the Φ<sub>Flow</sub> library.\n",
    "\n",
    "*Hint: You can execute the cell below multiple times to get different results. Both `GaussianClash` and `GaussianForce` use random numbers internally.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Force: 1.460236 at 0.465551\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# --- Set up physics ---\n",
    "world = World()\n",
    "u0 = BurgersVelocity(domain, velocity=GaussianClash(1), viscosity=viscosity)\n",
    "u = world.add(u0, physics=Burgers(diffusion_substeps=4))\n",
    "force = world.add(FieldEffect(GaussianForce(1), ['velocity']))\n",
    "# --- Plot ---\n",
    "print('Force: %f at %f' % (force.field.amp[0], force.field.loc[0]))\n",
    "bplt.burgers_figure('Training data')\n",
    "plt.plot(u.velocity.data[0,:,0], color=bplt.gradient_color(0, step_count+1), linewidth=0.8)  # data[example, values, component]\n",
    "plt.legend(['Initial state in dark red, final state in dark blue.'])\n",
    "for frame in range(1, step_count + 1):\n",
    "    world.step(dt=dt)  # runs one simulation step\n",
    "    plt.plot(u.velocity.data[0,:,0], color=bplt.gradient_color(frame, step_count+1), linewidth=0.8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we define how many examples to generate and where to store them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_path = 'forced-burgers-clash'\n",
    "scene_count = 1000  # how many examples to generate (training + validation + test)\n",
    "batch_size = 100  # How many examples to generate in parallel"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following cell will generate and store the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "for batch_index in range(scene_count // batch_size):\n",
    "    scene = Scene.create(data_path, count=batch_size)\n",
    "    print(scene)\n",
    "    world = World()\n",
    "    u0 = BurgersVelocity(domain, velocity=GaussianClash(batch_size), viscosity=viscosity, batch_size=batch_size, name='burgers')\n",
    "    u = world.add(u0, physics=Burgers(diffusion_substeps=4))\n",
    "    force = world.add(FieldEffect(GaussianForce(batch_size), ['velocity']))\n",
    "    scene.write(world.state, frame=0)\n",
    "    for frame in range(1, step_count + 1):\n",
    "        world.step(dt=dt)\n",
    "        scene.write(world.state, frame=frame)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To delete the generated data, uncomment and run the cell below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#for scene in Scene.list(data_path): scene.remove()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Supervised Initialization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use a supervised observation loss to initialize the observation prediction (OP) networks.\n",
    "This teaches them to reproduce the simulations from the training data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from control.pde.burgers import BurgersPDE\n",
    "from control.control_training import ControlTraining\n",
    "from control.sequences import StaggeredSequence, RefinedSequence"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define what part of the data is used for training, validation and testing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "test_range = range(100)\n",
    "val_range = range(100, 200)\n",
    "train_range = range(200, 1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following cell trains all OP$_n \\,\\, \\forall n\\in\\{2,4,8,16,32\\}$.\n",
    "The `ControlTraining` class is used to set up the optimization problem.\n",
    "\n",
    "The loss for the supervised initialization is defined as the observation loss at the center frame.\n",
    "\n",
    "$\\boldsymbol L_o^\\textrm{sup} = \\left|\\mathrm{OP}[o(t_i),o(t_j)] - u^\\textrm{GT}\\left(\\frac{t_i+t_j}{2}\\right)\\right|^2.$\n",
    "\n",
    "Consequently, no sequence needs to be simulated (`sequence_class=None`) and an observation loss is required at frame $\\frac n 2$ (`obs_loss_frames=[n // 2]`).\n",
    "The pretrained network checkpoints are stored in `supervised_checkpoints`.\n",
    "\n",
    "*Note: The next cell will run for some time. You can skip it and load the pretrained networks instead (see instructions below).*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "supervised_checkpoints = {}\n",
    "\n",
    "for n in [2, 4, 8, 16, 32]:\n",
    "    app = ControlTraining(n,\n",
    "                          BurgersPDE(domain, viscosity, dt),\n",
    "                          datapath=data_path,\n",
    "                          val_range=val_range,\n",
    "                          train_range=train_range,\n",
    "                          trace_to_channel=lambda trace: 'burgers_velocity',\n",
    "                          obs_loss_frames=[n // 2],\n",
    "                          trainable_networks=['OP%d' % n],\n",
    "                          sequence_class=None,\n",
    "                          batch_size=100,\n",
    "                          view_size=20,\n",
    "                          learning_rate=1e-3,\n",
    "                          learning_rate_half_life=1000,\n",
    "                          dt=dt).prepare()\n",
    "    # show(app, force_launch=True)  # launches the Φ-Flow web interface\n",
    "    for i in range(3000):\n",
    "        app.progress()  # Run Optimization for one batch\n",
    "    supervised_checkpoints['OP%d' % n] = app.save_model()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "supervised_checkpoints"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you have already initialized the networks, you can simply copy the `supervised_checkpoints` by pasting the output above into the cell below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# supervised_checkpoints = "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or load the pretrained networks that are included in the repository by uncommenting and running the cell below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# supervised_checkpoints = {'OP%d'%n: '../networks/burgers/supervised/OP%d_3000'%n for n in [2,4,8,16,32]}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that we have not actually set up a simulation for the training. To evaluate the quality of our current solutions, we will use the `ControlTraining` class again but this time passing a `sequence_class`.\n",
    "With a sequence class, `ControlTraining` sets up the necessary physics steps and networks.\n",
    "Example sequence classes are `StaggeredSequence` and `RefinedSequence`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "supervised_staggered_app = ControlTraining(\n",
    "                            32,\n",
    "                            BurgersPDE(domain, viscosity, dt),\n",
    "                            datapath=data_path,\n",
    "                            val_range=val_range,\n",
    "                            train_range=train_range,\n",
    "                            trace_to_channel=lambda trace: 'burgers_velocity',\n",
    "                            obs_loss_frames=[],\n",
    "                            trainable_networks=[],\n",
    "                            sequence_class=StaggeredSequence,\n",
    "                            batch_size=100,\n",
    "                            view_size=20,\n",
    "                            learning_rate=1e-3,\n",
    "                            learning_rate_half_life=1000,\n",
    "                            dt=dt).prepare()\n",
    "supervised_staggered_app.load_checkpoints(supervised_checkpoints)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can have a look at the force required to exactly match the target in our test set.\n",
    "\n",
    "*Note:* The property `'Total Force'` is created by `BurgersPDE`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print('Total Force (supervised): %f' % supervised_staggered_app.infer_scalars(test_range)['Total Force'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's have a look at some of the reconstructed sequences. Change the `test_range` indices to look at different examples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "states = supervised_staggered_app.infer_all_frames(test_range[0:1])\n",
    "bplt.burgers_figure('Supervised')\n",
    "for frame in range(0, step_count + 1):\n",
    "    plt.plot(states[frame].burgers.velocity.data[0,:,0], color=bplt.gradient_color(frame, step_count+1), linewidth=0.8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# End-to-end Training with Differentiable Physics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To initiale training with the differentiable physics loss, we create a new `ControlTraining` instance with the staggered execution scheme.\n",
    "\n",
    "The following cell trains all OP networks jointly to minimize the force (see the `trainable_networks` parameter). You can increase the number of optimization steps or execute the next cell multiple times to further increase performance.\n",
    "\n",
    "*Note: The next cell will run for some time. You can skip the next two cells and load the pretrained networks instead.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "staggered_app = ControlTraining(\n",
    "                            32,\n",
    "                            BurgersPDE(domain, viscosity, dt),\n",
    "                            datapath=data_path,\n",
    "                            val_range=val_range,\n",
    "                            train_range=train_range,\n",
    "                            trace_to_channel=lambda trace: 'burgers_velocity',\n",
    "                            obs_loss_frames=[],\n",
    "                            trainable_networks=['OP%d' % n for n in [2,4,8,16,32]],\n",
    "                            sequence_class=StaggeredSequence,\n",
    "                            batch_size=100,\n",
    "                            view_size=20,\n",
    "                            learning_rate=1e-3,\n",
    "                            learning_rate_half_life=1000,\n",
    "                            dt=dt).prepare()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "for i in range(3000):\n",
    "    staggered_app.progress()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "staggered_checkpoint = staggered_app.save_model()\n",
    "staggered_checkpoint"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To load the pretrained networks included in this repository, uncomment and execute the cell below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#staggered_app.load_checkpoints({'OP%d'%n: '../networks/burgers/staggered/OPn_18000' for n in [2,4,8,16,32]})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's evaluate the performance of our networks after end-to-end training."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print('Total Force (diff. phys. / staggered): %f' % staggered_app.infer_scalars(test_range)['Total Force'])\n",
    "states = staggered_app.infer_all_frames(test_range[0:1])\n",
    "bplt.burgers_figure('Staggered execution')\n",
    "for frame in range(0, step_count + 1):\n",
    "    plt.plot(states[frame].burgers.velocity.data[0,:,0], color=bplt.gradient_color(frame, step_count+1), linewidth=0.8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To evaluate our models using the prediction refinement scheme, we repeat the above steps but using a `RefinedSequence` instead of a `StaggeredSequence`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "refined_app = ControlTraining(step_count,\n",
    "                      BurgersPDE(domain, viscosity, dt),\n",
    "                      datapath=data_path,\n",
    "                      val_range=val_range,\n",
    "                      train_range=train_range,\n",
    "                      trace_to_channel=lambda trace: 'burgers_velocity',\n",
    "                      obs_loss_frames=[],\n",
    "                      trainable_networks=['OP%d' % n for n in [2,4,8,16,32]],\n",
    "                      sequence_class=RefinedSequence,\n",
    "                      batch_size=100,\n",
    "                      view_size=20,\n",
    "                      learning_rate=1e-3,\n",
    "                      learning_rate_half_life=1000,\n",
    "                      dt=dt).prepare()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To load the weights we just trained, run the cell below.\n",
    "\n",
    "To load the pretrained weights, skip the next cell and uncomment and run the one after that."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "refined_app.load_checkpoints({'OP%d' % n: staggered_checkpoint for n in [2,4,8,16,32]})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#refined_app.load_checkpoints({'OP%d'%n: '../networks/burgers/staggered/OPn_18000' for n in [2,4,8,16,32]})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We could still refine training at this point by repeatedly calling `refined_app.progress()`.\n",
    "Here, we show that the prediction refinement scheme beats the staggered execution, despite not being trained with that architecture."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print('Total Force (diff. phys. / refined): %f' % refined_app.infer_scalars(test_range)['Total Force'])\n",
    "states = refined_app.infer_all_frames(test_range[0:1])\n",
    "bplt.burgers_figure('Prediction refinement')\n",
    "for frame in range(0, step_count + 1):\n",
    "    plt.plot(states[frame].burgers.velocity.data[0,:,0], color=bplt.gradient_color(frame, step_count+1), linewidth=0.8)"
   ]
  }
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