added diff phys ns case
This commit is contained in:
NT
parent
8a0fadffc8
commit
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_toc.yml
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_toc.yml
@ -15,6 +15,7 @@
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sections:
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- file: diffphys-code-gradient.ipynb
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- file: diffphys-code-tf.ipynb
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- file: diffphys-code-ns.ipynb
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- file: jupyter-book-reference
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sections:
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- file: markdown
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@ -4,7 +4,7 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Burgers Optimizationwith a Gradient Differentiable Physics\n",
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"# Burgers Optimization with a Gradient from Differentiable Physics\n",
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"\n",
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"manual!\n",
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"\n",
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400
diffphys-code-ns.ipynb
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400
diffphys-code-ns.ipynb
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@ -0,0 +1,400 @@
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{
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"nbformat": 4,
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"nbformat_minor": 0,
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"metadata": {
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"colab": {
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"name": "Differentiable Fluid Simulations with Φ-Flow.ipynb",
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"provenance": [],
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"collapsed_sections": []
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},
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"kernelspec": {
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"name": "python3",
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"display_name": "Python 3"
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}
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},
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "o4JZ84moBKMr"
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},
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"source": [
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"# Differentiable Fluid Simulations with Φ<sub>Flow</sub>\n",
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"\n",
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"This notebook steps you through setting up fluid simulations and using TensorFlow's differentiation to optimize them.\n",
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"\n",
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"Execute the cell below to install the [Φ<sub>Flow</sub> Python package from GitHub](https://github.com/tum-pbs/PhiFlow)."
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"id": "Z6YoAVKebfNV"
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},
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"source": [
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"!pip install --upgrade --quiet phiflow"
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],
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "code",
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"metadata": {
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"id": "da1uZcDXdVcF"
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},
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"source": [
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"from phi.flow import * # The Dash GUI is not supported on Google Colab, ignore the warning\n",
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"import pylab"
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],
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "BVV1IKVqDfLl"
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},
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"source": [
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"# Setting up a simulation\n",
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"\n",
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"Φ<sub>Flow</sub> is object-oriented, i.e. you assemble your simulation by constructing a number of objects and adding them to the world.\n",
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"\n",
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"The following code sets up four fluid simulations that run in parallel (`batch_size=4`). Each fluid simulation has a circular Inflow at a different location."
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"id": "WrA3IXDxv31P"
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},
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"source": [
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"world = World()\n",
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"fluid = world.add(Fluid(Domain([40, 32], boundaries=CLOSED), buoyancy_factor=0.1, batch_size=4), physics=IncompressibleFlow())\n",
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"world.add(Inflow(Sphere(center=[[5,4], [5,8], [5,12], [5,16]], radius=3), rate=0.2));"
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],
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "ExA0Pi2sFVka"
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},
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"source": [
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"The inflow affects the fluid's marker density. Because the `buoyancy_factor` is positive, the marker creates an upward force.\n",
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"\n",
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"Let's plot the marker density after one simulation frame."
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"id": "WmGZdOwswOva"
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},
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"source": [
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"world.step()\n",
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"pylab.imshow(np.concatenate(fluid.density.data[...,0], axis=1), origin='lower', cmap='magma')"
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],
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "PA-2tGuWGHv2"
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},
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"source": [
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"We can run more steps by repeatedly calling `world.step()`."
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"id": "0hZk5HX3w4Or"
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},
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"source": [
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"for frame in range(20):\n",
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" print('Computing frame %d' % frame)\n",
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" world.step(dt=1.5)"
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],
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "code",
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"metadata": {
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"id": "Mfl80CjZxZcL"
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},
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"source": [
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"pylab.imshow(np.concatenate(fluid.density.data[...,0], axis=1), origin='lower', cmap='magma')"
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],
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "rdSTbMoaS0Uz"
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},
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"source": [
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"# Differentiation\n",
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"\n",
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"The simulation we just computed was using purely NumPy (non-differentiable) operations.\n",
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"To enable differentiability, we need to build a TensorFlow graph that computes this result."
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"id": "mphMP0sYIOz-"
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},
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"source": [
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"%tensorflow_version 1.x\n",
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"from phi.tf.flow import * # Causes deprecation warnings with TF 1.15\n",
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"import pylab\n",
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"session = Session(None) # Used to run the TensorFlow graph"
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],
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "3mpyowRYUSS4"
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},
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"source": [
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"Let's set up the simulation just like before. But now, we want to optimize the initial velocities so that all simulations arrive at a final state that is similar to the first simulation from the previous example. I.e., the state shown in the left-most image above.\n",
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"\n",
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"To achieve this, we create a TensorFlow variable for the velocity at t=0.\n",
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"It is initialized with zeros (like with the NumPy simulation above) and can later be used as a target for optimization."
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"id": "NlJMJikaHOL6"
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},
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"source": [
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"world = World()\n",
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"fluid = world.add(Fluid(Domain([40, 32], boundaries=CLOSED), buoyancy_factor=0.1, batch_size=4), physics=IncompressibleFlow())\n",
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"world.add(Inflow(Sphere(center=[[5,4], [5,8], [5,12], [5,16]], radius=3), rate=0.2));\n",
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"fluid.velocity = variable(fluid.velocity) # create TensorFlow variable\n",
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"initial_state = fluid.state # Remember the state at t=0 for later visualization\n",
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"session.initialize_variables()"
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],
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "t-NDwXRCYHjw"
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},
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"source": [
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"\n",
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"\n",
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"Note that we actually created two variables, one for each velocity component. If you're interested in how this magic works, have a look at the [Struct documentation](https://github.com/tum-pbs/PhiFlow/blob/master/documentation/Structs.ipynb)."
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"id": "2q5gfaH2YHr6"
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},
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"source": [
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"[print(grid.data) for grid in fluid.velocity.unstack()];"
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],
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "vSdGIEzCgq5-"
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},
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"source": [
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"If you look closely, you'll notice that the shapes of the variables differ. This is because the velocity is sampled in [staggered form](https://github.com/tum-pbs/PhiFlow/blob/master/documentation/Staggered_Grids.md).\n",
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"\n",
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"The simulation now contains variables in the initial state.\n",
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"Since all later states depend on the value of the variable, the `step` method cannot directly compute concrete state values.\n",
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"Instead, `world.step` will extend the TensorFlow graph by the operations needed to perform the step.\n",
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"\n",
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"To execute the graph with actual data, we can use `session.run`, just like with regular TensorFlow 1.x. While `run` would usually be used to infer predictions from a learning model, it now executes the graph of simulation steps."
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"id": "wSrIezfWHjcQ"
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},
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"source": [
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"world.step()\n",
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"pylab.imshow(np.concatenate(session.run(fluid.density).data[...,0], axis=1), origin='lower', cmap='magma')"
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],
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "iJc6UdYHhtOH"
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},
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"source": [
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"Let's build a graph for the full simulation."
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"id": "b9xHtdDQRrjL"
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},
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"source": [
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"for frame in range(20):\n",
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" print('Building graph for frame %d' % frame)\n",
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" world.step(dt=1.5)"
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],
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "2VQ92g2rs6wM"
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},
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"source": [
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"When calling `session.run` now, the full simulation is evaluated using TensorFlow operations.\n",
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"This will take advantage of your GPU, if available.\n",
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"If you compile Φ<sub>Flow</sub> with [CUDA support](https://github.com/tum-pbs/PhiFlow/blob/master/documentation/Installation_Instructions.md), the TensorFlow graph will use optimized operators for efficient simulation and training runs."
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"id": "TA6Ibs-mXsTc"
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},
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"source": [
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"print('Computing frames...')\n",
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"pylab.imshow(np.concatenate(session.run(fluid.density).data[...,0], axis=1), origin='lower', cmap='magma')"
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],
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "IClfRMfoyGUa"
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},
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"source": [
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"Next, we define the *loss* function (also called *cost* or *objective* function). This is the value we want to decrease via optimization.\n",
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"For this example, we want the marker densities of all final simulation states to match the left-most one, called `target`.\n",
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"\n",
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"For the optimizer, we choose gradient descent for this example."
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"id": "7KPpyIwjYETi"
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},
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"source": [
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"target = session.run(fluid.density).data[0,...]\n",
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"loss = math.l2_loss(fluid.density.data[1:,...] - target)\n",
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"optim = tf.train.GradientDescentOptimizer(learning_rate=0.1).minimize(loss)\n",
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"session.initialize_variables()\n",
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"print('Initial loss: %f' % session.run(loss))"
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],
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "AALD66-N0U5F"
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},
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"source": [
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"With the loss and optimizer set up, all that's left is to run the actual optimization."
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"id": "pvvF6xqmaRLX"
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},
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"source": [
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"for optim_step in range(10):\n",
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" print('Running optimization step %d. %s' % (optim_step, '' if optim_step else 'The first step sets up the adjoint graph.'))\n",
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" _, loss_value = session.run([optim, loss])\n",
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" print('Loss: %f' % loss_value)"
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],
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "code",
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"metadata": {
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"id": "SQBtCmhZaYYj"
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},
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"source": [
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"pylab.imshow(np.concatenate(session.run(fluid.density).data[...,0], axis=1), origin='lower', cmap='magma')"
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],
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "HP7aDQfpKifp"
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},
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"source": [
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"Now that the optimization has done its work, we can have a look at the now-optimized initial velocity field."
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"id": "vRaBt5vGdSEY"
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},
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"source": [
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"optimized_velocity_field = session.run(initial_state.velocity).at_centers()"
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],
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "code",
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"metadata": {
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"id": "i7ZahlUudex8"
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},
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"source": [
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"pylab.title('Initial y-velocity (optimized)')\n",
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"pylab.imshow(np.concatenate(optimized_velocity_field.data[...,0], axis=1), origin='lower')"
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],
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "code",
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"metadata": {
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"id": "Pqw5BDxmdkut"
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},
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"source": [
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"pylab.title('Initial x-velocity (optimized)')\n",
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"pylab.imshow(np.concatenate(optimized_velocity_field.data[...,1], axis=1), origin='lower')"
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],
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "ooqVxCPM8PXl"
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},
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"source": [
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"This notebook provided an introduction to running fluid simulations in NumPy and TensorFlow.\n",
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"It demonstrated how to use the gradients provided by Φ<sub>Flow</sub> to run simple optimizations over the course of several timesteps.\n",
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"\n",
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"For additional examples, e.g. coupling simulations with neural networks, please check the [other demos](https://github.com/tum-pbs/PhiFlow/tree/master/demos)."
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]
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}
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]
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}
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@ -4,7 +4,7 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Burgers backwards opt in phiflow-TF optim\n",
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"# Burgers backwards opt via phiflow-TF optim\n",
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"\n",
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"Use actual TF optimizer"
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]
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