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upd intro parabola, cleanup

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NT
2021-01-31 12:13:00 +08:00
parent e3e72982a7
commit 4e9149becf
10 changed files with 1433 additions and 989 deletions
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5
_toc.yml
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@@ -1,6 +1,8 @@
# PBDL Table of content (cf https://jupyterbook.org/customize/toc.html)
#
- file: intro
- file: intro.md
sections:
- file: intro-teaser.ipynb
- file: overview.md
sections:
- file: overview-equations.md
@@ -21,6 +23,7 @@
- file: diffphys-discuss.md
- file: diffphys-code-ns.ipynb
- file: diffphys-code-sol.ipynb
- file: diffphys-outlook.md
- file: jupyter-book-reference
sections:
- file: markdown

13
diffphys-code-ns.ipynb
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@@ -9,15 +9,16 @@
"# Differentiable Fluid Simulations\n",
"\n",
"Next, we'll target a more complex example with the Navier-Stokes equations as model. We'll target a 2D case with velocity $\\mathbf{u}$, no explicit viscosity term, and a marker density $d$ that drives a simple Boussinesq buoyancy term $\\eta d$ adding a force along the y dimension:\n",
"$\n",
" \\frac{\\partial u_x}{\\partial{t}} + \\mathbf{u} \\cdot \\nabla u_x = - \\frac{1}{\\rho} \\nabla p \n",
"\n",
"$\\begin{aligned}\n",
" \\frac{\\partial u_x}{\\partial{t}} + \\mathbf{u} \\cdot \\nabla u_x &= - \\frac{1}{\\rho} \\nabla p \n",
" \\\\\n",
" \\frac{\\partial u_y}{\\partial{t}} + \\mathbf{u} \\cdot \\nabla u_y = - \\frac{1}{\\rho} \\nabla p + \\eta d\n",
" \\frac{\\partial u_y}{\\partial{t}} + \\mathbf{u} \\cdot \\nabla u_y &= - \\frac{1}{\\rho} \\nabla p + \\eta d\n",
" \\\\\n",
" \\text{subject to} \\quad \\nabla \\cdot \\mathbf{u} = 0,\n",
" \\text{s.t.} \\quad \\nabla \\cdot \\mathbf{u} &= 0,\n",
" \\\\\n",
" \\frac{\\partial d}{\\partial{t}} + \\mathbf{u} \\cdot \\nabla d = 0 \n",
"$\n",
" \\frac{\\partial d}{\\partial{t}} + \\mathbf{u} \\cdot \\nabla d &= 0 \n",
"\\end{aligned}$\n",
"\n",
"As optimization objective we'll consider a more difficult variant of the previous example: the state of the observed density $d$ should match a given target after $n=20$ steps of simulation. In contrast to before, the marker $d$ cannot be modified in any way, but only the initial state of the velocity $\\mathbf{u}$ at $t=0$. This gives us a split between observable quantities for the loss formulation, and quantities that we can interact with during the optimization (or later on via NNs).\n",
"\n",

357
diffphys-code-sol.ipynb
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@@ -1,17 +1,4 @@
{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "diffphys-code-sol.ipynb",
"provenance": [],
"collapsed_sections": []
},
"kernelspec": {
"display_name": "Python 3",
"name": "python3"
}
},
"cells": [
{
"cell_type": "markdown",
@@ -113,6 +100,7 @@
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
@@ -120,6 +108,16 @@
"id": "JwZudtWauiGa",
"outputId": "bd3a4a4d-706f-4210-ee4e-ca4e370b762d"
},
"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\n",
"\n",
@@ -131,17 +129,6 @@
"\n",
"with open('data-karman2d-train.pickle', 'rb') as f: dataPreloaded = pickle.load(f)\n",
"print(\"Loaded data, {} training sims\".format(len(dataPreloaded)) )\n"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"text": [
"Downloading training data (73MB), this can take a moment the first time...\n",
"Loaded data, 6 training sims\n"
],
"name": "stdout"
}
]
},
{
@@ -155,6 +142,7 @@
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
@@ -162,6 +150,36 @@
"id": "BGN4GqxkIueM",
"outputId": "095adbf8-1ef6-41fd-938e-6cafcf0fdfdc"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\u001b[K |████████████████████████████████| 2.7MB 4.3MB/s \n",
"\u001b[?25h Building wheel for phiflow (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
"TensorFlow 1.x selected.\n",
"Could not load resample cuda libraries: CUDA binaries not found at /usr/local/lib/python3.6/dist-packages/phi/tf/cuda/build/resample.so. Run \"python setup.py cuda\" to compile them\n",
"WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/phi/tf/util.py:119: The name tf.AUTO_REUSE is deprecated. Please use tf.compat.v1.AUTO_REUSE instead.\n",
"\n",
"WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/phi/tf/profiling.py:12: The name tf.RunOptions is deprecated. Please use tf.compat.v1.RunOptions instead.\n",
"\n",
"WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/phi/tf/profiling.py:13: The name tf.RunMetadata is deprecated. Please use tf.compat.v1.RunMetadata instead.\n",
"\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/usr/local/lib/python3.6/dist-packages/phi/viz/display.py:80: UserWarning: GUI is disabled because of missing dependencies: No module named 'dash_core_components'. To install all dependencies, run $ pip install phiflow[gui]\n",
" warnings.warn('GUI is disabled because of missing dependencies: %s. To install all dependencies, run $ pip install phiflow[gui]' % import_error)\n",
"/usr/local/lib/python3.6/dist-packages/phi/tf/flow.py:15: UserWarning: TensorFlow-CUDA solver is not available. To compile it, download phiflow sources and run\n",
"$ python setup.py tf_cuda\n",
"before reinstalling phiflow.\n",
" warnings.warn(\"TensorFlow-CUDA solver is not available. To compile it, download phiflow sources and run\\n$ python setup.py tf_cuda\\nbefore reinstalling phiflow.\")\n"
]
}
],
"source": [
"!pip install --upgrade --quiet phiflow\n",
"%tensorflow_version 1.x\n",
@@ -175,37 +193,6 @@
"random.seed(42)\n",
"np.random.seed(42)\n",
"tf.compat.v1.set_random_seed(42)\n"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"text": [
"\u001b[K |████████████████████████████████| 2.7MB 4.3MB/s \n",
"\u001b[?25h Building wheel for phiflow (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
"TensorFlow 1.x selected.\n",
"Could not load resample cuda libraries: CUDA binaries not found at /usr/local/lib/python3.6/dist-packages/phi/tf/cuda/build/resample.so. Run \"python setup.py cuda\" to compile them\n",
"WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/phi/tf/util.py:119: The name tf.AUTO_REUSE is deprecated. Please use tf.compat.v1.AUTO_REUSE instead.\n",
"\n",
"WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/phi/tf/profiling.py:12: The name tf.RunOptions is deprecated. Please use tf.compat.v1.RunOptions instead.\n",
"\n",
"WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/phi/tf/profiling.py:13: The name tf.RunMetadata is deprecated. Please use tf.compat.v1.RunMetadata instead.\n",
"\n"
],
"name": "stdout"
},
{
"output_type": "stream",
"text": [
"/usr/local/lib/python3.6/dist-packages/phi/viz/display.py:80: UserWarning: GUI is disabled because of missing dependencies: No module named 'dash_core_components'. To install all dependencies, run $ pip install phiflow[gui]\n",
" warnings.warn('GUI is disabled because of missing dependencies: %s. To install all dependencies, run $ pip install phiflow[gui]' % import_error)\n",
"/usr/local/lib/python3.6/dist-packages/phi/tf/flow.py:15: UserWarning: TensorFlow-CUDA solver is not available. To compile it, download phiflow sources and run\n",
"$ python setup.py tf_cuda\n",
"before reinstalling phiflow.\n",
" warnings.warn(\"TensorFlow-CUDA solver is not available. To compile it, download phiflow sources and run\\n$ python setup.py tf_cuda\\nbefore reinstalling phiflow.\")\n"
],
"name": "stderr"
}
]
},
{
@@ -238,9 +225,11 @@
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "6WNMcdWUw4EP"
},
"outputs": [],
"source": [
"class KarmanFlow(IncompressibleFlow):\n",
" def __init__(self, pressure_solver=None, make_input_divfree=False, make_output_divfree=True):\n",
@@ -262,9 +251,7 @@
" fluid = fluid.copied_with(velocity=StaggeredGrid([cy.data, cx.data], fluid.velocity.box))\n",
"\n",
" return super().step(fluid=fluid, dt=dt, obstacles=[self.obst], gravity=gravity, density_effects=[self.infl], velocity_effects=())\n"
],
"execution_count": null,
"outputs": []
]
},
{
"cell_type": "markdown",
@@ -290,9 +277,11 @@
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "qIrWYTy6xscA"
},
"outputs": [],
"source": [
"def network_small(tensor_in):\n",
" return keras.Sequential([\n",
@@ -301,9 +290,7 @@
" keras.layers.Conv2D(filters=64, kernel_size=5, padding='same', activation=tf.nn.relu),\n",
" keras.layers.Conv2D(filters=2, kernel_size=5, padding='same', activation=None), # u, v\n",
" ])\n"
],
"execution_count": null,
"outputs": []
]
},
{
"cell_type": "markdown",
@@ -316,9 +303,11 @@
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "TyfpA7Fbx0ro"
},
"outputs": [],
"source": [
"def network_medium(tensor_in):\n",
" l_input = keras.layers.Input(tensor=tensor_in)\n",
@@ -357,9 +346,7 @@
"\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"
],
"execution_count": null,
"outputs": []
]
},
{
"cell_type": "markdown",
@@ -376,9 +363,11 @@
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "hhGFpTjGyRyg"
},
"outputs": [],
"source": [
"def to_keras(fluidstate, ext_const_channel):\n",
" # drop the unused edges of the staggered velocity grid making its dim same to the centered grid's\n",
@@ -392,9 +381,7 @@
"\n",
"def to_staggered(tensor_cen, box):\n",
" return StaggeredGrid(math.pad(tensor_cen, ((0,0), (0,1), (0,1), (0,0))), box=box)\n"
],
"execution_count": null,
"outputs": []
]
},
{
"cell_type": "markdown",
@@ -415,9 +402,11 @@
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "tjywcdD2y20t"
},
"outputs": [],
"source": [
"class Dataset():\n",
" def __init__(self, data_preloaded, num_frames, num_sims=None, batch_size=1):\n",
@@ -484,9 +473,7 @@
"\n",
" def nextStep(self):\n",
" self.stepIdx += 1\n"
],
"execution_count": null,
"outputs": []
]
},
{
"cell_type": "markdown",
@@ -501,9 +488,11 @@
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "Dfwd4TnqN1Tn"
},
"outputs": [],
"source": [
" # for class Dataset():\n",
"\n",
@@ -535,9 +524,7 @@
" ][0] for i in range(self.batchSize)\n",
" ]\n",
" return [marker_dens, velocity, ext]\n"
],
"execution_count": null,
"outputs": []
]
},
{
"cell_type": "markdown",
@@ -550,6 +537,7 @@
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
@@ -557,6 +545,15 @@
"id": "59EBdEdj0QR2",
"outputId": "8043f090-4e7b-4178-d2d2-513981e3905b"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Data stats: {'std': (2.2194703, (0.32598782, 0.1820292)), 'ext.std': [1732512.6262166172]}\n"
]
}
],
"source": [
"output_dir = \"./\" # TODO create? , replaced params['train'] and params['tf']\n",
"nsims = 6\n",
@@ -567,16 +564,6 @@
"#dataset.newEpoch()\n",
"#print(format(getData(dataset,1)))\n",
"#print(format(dataset.getData(1)))\n"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"text": [
"Data stats: {'std': (2.2194703, (0.32598782, 0.1820292)), 'ext.std': [1732512.6262166172]}\n"
],
"name": "stdout"
}
]
},
{
@@ -594,6 +581,7 @@
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
@@ -601,6 +589,39 @@
"id": "EjgkdCzKP2Ip",
"outputId": "6b21bd54-15aa-4440-b274-c3a68ab244f8"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"WARNING:tensorflow:From /tensorflow-1.15.2/python3.6/tensorflow_core/python/ops/resource_variable_ops.py:1630: calling BaseResourceVariable.__init__ (from tensorflow.python.ops.resource_variable_ops) with constraint is deprecated and will be removed in a future version.\n",
"Instructions for updating:\n",
"If using Keras pass *_constraint arguments to layers.\n",
"Model: \"sequential\"\n",
"_________________________________________________________________\n",
"Layer (type) Output Shape Param # \n",
"=================================================================\n",
"conv2d (Conv2D) (3, 64, 32, 32) 2432 \n",
"_________________________________________________________________\n",
"conv2d_1 (Conv2D) (3, 64, 32, 64) 51264 \n",
"_________________________________________________________________\n",
"conv2d_2 (Conv2D) (3, 64, 32, 2) 3202 \n",
"=================================================================\n",
"Total params: 56,898\n",
"Trainable params: 56,898\n",
"Non-trainable params: 0\n",
"_________________________________________________________________\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:23: DeprecationWarning: placeholder_like may not respect the batch dimension. For State objects, use placeholder(state.shape) instead.\n",
"/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:24: DeprecationWarning: placeholder_like may not respect the batch dimension. For State objects, use placeholder(state.shape) instead.\n"
]
}
],
"source": [
"# one of the most crucial! how many simulation steps to look into the future while training\n",
"msteps = 4\n",
@@ -631,40 +652,6 @@
"#network = network_medium(to_keras(source_in, Re_in)) # optionally switch to larger network\n",
"network.summary() \n",
"\n"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"text": [
"WARNING:tensorflow:From /tensorflow-1.15.2/python3.6/tensorflow_core/python/ops/resource_variable_ops.py:1630: calling BaseResourceVariable.__init__ (from tensorflow.python.ops.resource_variable_ops) with constraint is deprecated and will be removed in a future version.\n",
"Instructions for updating:\n",
"If using Keras pass *_constraint arguments to layers.\n",
"Model: \"sequential\"\n",
"_________________________________________________________________\n",
"Layer (type) Output Shape Param # \n",
"=================================================================\n",
"conv2d (Conv2D) (3, 64, 32, 32) 2432 \n",
"_________________________________________________________________\n",
"conv2d_1 (Conv2D) (3, 64, 32, 64) 51264 \n",
"_________________________________________________________________\n",
"conv2d_2 (Conv2D) (3, 64, 32, 2) 3202 \n",
"=================================================================\n",
"Total params: 56,898\n",
"Trainable params: 56,898\n",
"Non-trainable params: 0\n",
"_________________________________________________________________\n"
],
"name": "stdout"
},
{
"output_type": "stream",
"text": [
"/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:23: DeprecationWarning: placeholder_like may not respect the batch dimension. For State objects, use placeholder(state.shape) instead.\n",
"/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:24: DeprecationWarning: placeholder_like may not respect the batch dimension. For State objects, use placeholder(state.shape) instead.\n"
],
"name": "stderr"
}
]
},
{
@@ -682,9 +669,11 @@
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "D5NeMcLGQaxh"
},
"outputs": [],
"source": [
"prediction, correction = [], []\n",
"for i in range(msteps):\n",
@@ -711,9 +700,7 @@
" ]\n",
"\n",
" prediction[-1] = prediction[-1].copied_with(velocity=prediction[-1].velocity + correction[-1])\n"
],
"execution_count": null,
"outputs": []
]
},
{
"cell_type": "markdown",
@@ -726,9 +713,11 @@
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "K2JcO3-QQgC9"
},
"outputs": [],
"source": [
"loss_steps = [\n",
" tf.nn.l2_loss(\n",
@@ -738,9 +727,7 @@
" for i in range(msteps)\n",
"]\n",
"loss = tf.reduce_sum(loss_steps)/msteps\n"
],
"execution_count": null,
"outputs": []
]
},
{
"cell_type": "markdown",
@@ -755,9 +742,11 @@
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "PuljFamYQksW"
},
"outputs": [],
"source": [
"lr = 1e-4\n",
"adapt_lr = True\n",
@@ -778,9 +767,7 @@
"if resume>0: \n",
" ld_network = keras.models.load_model(output_dir+'/nn_epoch{:04d}.h5'.format(resume))\n",
" network.set_weights(ld_network.get_weights())\n"
],
"execution_count": null,
"outputs": []
]
},
{
"cell_type": "markdown",
@@ -793,9 +780,11 @@
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "Am3hSdNgRPEh"
},
"outputs": [],
"source": [
"\n",
"def lr_schedule(epoch, current_lr):\n",
@@ -805,9 +794,7 @@
" elif epoch == 15: lr *= 1e-1\n",
" elif epoch == 10: lr *= 1e-1\n",
" return lr\n"
],
"execution_count": null,
"outputs": []
]
},
{
"cell_type": "markdown",
@@ -822,50 +809,17 @@
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "m3Nd8YyHRVFQ",
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "m3Nd8YyHRVFQ",
"outputId": "148d951b-7070-4a95-c6d7-0fd91d29606e"
},
"source": [
"current_lr = lr\n",
"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",
" current_lr = lr_schedule(j, current_lr) if adapt_lr else lr\n",
" for ib in range(dataset.numBatches): \n",
" for i in range(dataset.numSteps): \n",
" batch = getData(dataset, consecutive_frames=msteps) # should be dataset.getData\n",
" re_nr = batch[2] # Reynolds numbers\n",
" source = source.copied_with(density=batch[0][0], velocity=batch[1][0])\n",
" reference = [ reference[k].copied_with(density=batch[0][k+1], velocity=batch[1][k+1]) for k in range(msteps) ]\n",
"\n",
" my_feed_dict = { source_in: source, Re_in: re_nr, lr_in: current_lr }\n",
" my_feed_dict.update(zip(reference_in, reference))\n",
" _, l2 = sess.run([train_step, loss], my_feed_dict)\n",
" steps += 1\n",
"\n",
" if (j==0 and i<3) or (j==0 and ib==0 and i%31==0) or (ib==0 and i%124==0):\n",
" print('epoch {:03d}/{:03d}, batch {:03d}/{:03d}, step {:04d}/{:04d}: loss={}'.format( j+1, epochs, ib+1, dataset.numBatches, i+1, dataset.numSteps, l2 ))\n",
" dataset.nextStep()\n",
"\n",
" dataset.nextBatch()\n",
"\n",
" if j%10==9: network.save(output_dir+'/nn_epoch{:04d}.h5'.format(j+1))\n",
"\n",
"# all done! save final version\n",
"network.save(output_dir+'/final.h5')\n"
],
"execution_count": null,
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"epoch 001/004, batch 001/002, step 0001/0496: loss=8114.626953125\n",
@@ -901,9 +855,42 @@
"epoch 004/004, batch 001/002, step 0125/0496: loss=4.158570289611816\n",
"epoch 004/004, batch 001/002, step 0249/0496: loss=4.282064437866211\n",
"epoch 004/004, batch 001/002, step 0373/0496: loss=5.2111334800720215\n"
],
"name": "stdout"
]
}
],
"source": [
"current_lr = lr\n",
"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",
" current_lr = lr_schedule(j, current_lr) if adapt_lr else lr\n",
" for ib in range(dataset.numBatches): \n",
" for i in range(dataset.numSteps): \n",
" batch = getData(dataset, consecutive_frames=msteps) # should be dataset.getData\n",
" re_nr = batch[2] # Reynolds numbers\n",
" source = source.copied_with(density=batch[0][0], velocity=batch[1][0])\n",
" reference = [ reference[k].copied_with(density=batch[0][k+1], velocity=batch[1][k+1]) for k in range(msteps) ]\n",
"\n",
" my_feed_dict = { source_in: source, Re_in: re_nr, lr_in: current_lr }\n",
" my_feed_dict.update(zip(reference_in, reference))\n",
" _, l2 = sess.run([train_step, loss], my_feed_dict)\n",
" steps += 1\n",
"\n",
" if (j==0 and i<3) or (j==0 and ib==0 and i%31==0) or (ib==0 and i%124==0):\n",
" print('epoch {:03d}/{:03d}, batch {:03d}/{:03d}, step {:04d}/{:04d}: loss={}'.format( j+1, epochs, ib+1, dataset.numBatches, i+1, dataset.numSteps, l2 ))\n",
" dataset.nextStep()\n",
"\n",
" dataset.nextBatch()\n",
"\n",
" if j%10==9: network.save(output_dir+'/nn_epoch{:04d}.h5'.format(j+1))\n",
"\n",
"# all done! save final version\n",
"network.save(output_dir+'/final.h5')\n"
]
},
{
@@ -933,14 +920,38 @@
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "RumKebW_05xp"
},
"source": [
""
],
"execution_count": null,
"outputs": []
"outputs": [],
"source": []
}
]
],
"metadata": {
"colab": {
"collapsed_sections": [],
"name": "diffphys-code-sol.ipynb",
"provenance": []
},
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 1
}

418
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16
intro.md
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@@ -15,11 +15,12 @@ more tightly coupled learning algorithms with differentiable simulations.
height: 220px
name: pbdl-teaser
---
Some examples ... preview teaser ...
Some visual examples of hybrid solvers, i.e. numerical simulators that are enhanced by trained neural networks.
```
% Teaser, simple version:
% ![Teaser, simple version](resources/teaser.png)
## Coming up
As a _sneak preview_, in the next chapters we'll show:
@@ -38,9 +39,6 @@ and we're eager to improve it. Thanks in advance!
This collection of materials is a living document, and will grow and change over time.
Feel free to contribute 😀
[TUM Physics-based Simulation Group](https://ge.in.tum.de).
We also maintain a [link collection](https://github.com/thunil/Physics-Based-Deep-Learning) with recent research papers.
```{admonition} Code, executable, right here, right now
@@ -52,16 +50,6 @@ immediately see what happens -- give it a try...
Oh, and it's great because it's [literate programming](https://en.wikipedia.org/wiki/Literate_programming).
```
## More Specifically
To be a bit more specific, _physics_ is a huge field, and we can't cover everything...
```{note}
For now our focus is:
- field-based simulations , less Lagrangian
- simulations, not experiments
- combination with _deep learning_ (plenty of other interesting ML techniques)
```
---

49
overview-equations.md
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@@ -1,10 +1,12 @@
Model Equations
============================
overview of PDE models to be used later on ...
TODO
give an overview of PDE models to be used later on ...
continuous pde $\mathcal P^*$
$\vx \in \Omega \subseteq \mathbb{R}^d$
$\mathbf{x} \in \Omega \subseteq \mathbb{R}^d$
for the domain $\Omega$ in $d$ dimensions,
time $t \in \mathbb{R}^{+}$.
@@ -47,11 +49,8 @@ and the abbreviations used inn: {doc}`notation`, at the bottom of the left panel
% \newcommand{\corr}{\mathcal{C}} % just C for now...
% \newcommand{\nnfunc}{F} % {\text{NN}}
Some notation from SoL, move with parts from overview into "appendix"?
We typically solve a discretized PDE $\mathcal{P}$ by performing discrete time steps of size $\Delta t$.
Each subsequent step can depend on any number of previous steps,
$\mathbf{u}(\mathbf{x},t+\Delta t) = \mathcal{P}(\mathbf{u}(\mathbf{x},t), \mathbf{u}(\mathbf{x},t-\Delta t),...)$,
@@ -83,12 +82,13 @@ $\mathbf{u} = (u_x,u_y,u_z)^T$ for $d=3$.
Burgers' equation in 2D. It represents a well-studied advection-diffusion PDE:
$\frac{\partial u_x}{\partial{t}} + \mathbf{u} \cdot \nabla u_x =
$\begin{aligned}
\frac{\partial u_x}{\partial{t}} + \mathbf{u} \cdot \nabla u_x &=
\nu \nabla\cdot \nabla u_x + g_x(t),
\\
\frac{\partial u_y}{\partial{t}} + \mathbf{u} \cdot \nabla u_y =
\frac{\partial u_y}{\partial{t}} + \mathbf{u} \cdot \nabla u_y &=
\nu \nabla\cdot \nabla u_y + g_y(t)
$,
\end{aligned}$,
where $\nu$ and $\mathbf{g}$ denote diffusion constant and external forces, respectively.
@@ -104,15 +104,15 @@ Later on, additional equations...
Navier-Stokes, in 2D:
$
\frac{\partial u_x}{\partial{t}} + \mathbf{u} \cdot \nabla u_x =
$\begin{aligned}
\frac{\partial u_x}{\partial{t}} + \mathbf{u} \cdot \nabla u_x &=
- \frac{1}{\rho}\nabla{p} + \nu \nabla\cdot \nabla u_x
\\
\frac{\partial u_y}{\partial{t}} + \mathbf{u} \cdot \nabla u_y =
\frac{\partial u_y}{\partial{t}} + \mathbf{u} \cdot \nabla u_y &=
- \frac{1}{\rho}\nabla{p} + \nu \nabla\cdot \nabla u_y
\\
\text{subject to} \quad \nabla \cdot \mathbf{u} = 0
$
\text{subject to} \quad \nabla \cdot \mathbf{u} &= 0
\end{aligned}$
@@ -121,28 +121,29 @@ Navier-Stokes, in 2D with Boussinesq:
%$\frac{\partial u_x}{\partial{t}} + \mathbf{u} \cdot \nabla u_x$
%$ -\frac{1}{\rho} \nabla p $
$
\frac{\partial u_x}{\partial{t}} + \mathbf{u} \cdot \nabla u_x = - \frac{1}{\rho} \nabla p
$\begin{aligned}
\frac{\partial u_x}{\partial{t}} + \mathbf{u} \cdot \nabla u_x &= - \frac{1}{\rho} \nabla p
\\
\frac{\partial u_y}{\partial{t}} + \mathbf{u} \cdot \nabla u_y = - \frac{1}{\rho} \nabla p + \eta d
\frac{\partial u_y}{\partial{t}} + \mathbf{u} \cdot \nabla u_y &= - \frac{1}{\rho} \nabla p + \eta d
\\
\text{subject to} \quad \nabla \cdot \mathbf{u} = 0,
\text{subject to} \quad \nabla \cdot \mathbf{u} &= 0,
\\
\frac{\partial d}{\partial{t}} + \mathbf{u} \cdot \nabla d = 0
$
\frac{\partial d}{\partial{t}} + \mathbf{u} \cdot \nabla d &= 0
\end{aligned}$
Navier-Stokes, in 3D:
$
\frac{\partial u_x}{\partial{t}} + \mathbf{u} \cdot \nabla u_x = - \frac{1}{\rho} \nabla p + \nu \nabla\cdot \nabla u_x
\begin{aligned}
\frac{\partial u_x}{\partial{t}} + \mathbf{u} \cdot \nabla u_x &= - \frac{1}{\rho} \nabla p + \nu \nabla\cdot \nabla u_x
\\
\frac{\partial u_y}{\partial{t}} + \mathbf{u} \cdot \nabla u_y = - \frac{1}{\rho} \nabla p + \nu \nabla\cdot \nabla u_y
\frac{\partial u_y}{\partial{t}} + \mathbf{u} \cdot \nabla u_y &= - \frac{1}{\rho} \nabla p + \nu \nabla\cdot \nabla u_y
\\
\frac{\partial u_z}{\partial{t}} + \mathbf{u} \cdot \nabla u_z = - \frac{1}{\rho} \nabla p + \nu \nabla\cdot \nabla u_z
\frac{\partial u_z}{\partial{t}} + \mathbf{u} \cdot \nabla u_z &= - \frac{1}{\rho} \nabla p + \nu \nabla\cdot \nabla u_z
\\
\text{subject to} \quad \nabla \cdot \mathbf{u} = 0.
\text{subject to} \quad \nabla \cdot \mathbf{u} &= 0.
\end{aligned}
$

22
overview.md
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@@ -11,6 +11,8 @@ a starting point for new researchers as well as a hands-on introduction into
state-of-the-art resarch topics.
```{figure} resources/overview-pano.jpg
---
height: 240px
@@ -127,6 +129,21 @@ starting points with code examples, and illustrate pros and cons of the
different approaches. In particular, it's important to know in which scenarios
each of the different techniques is particularly useful.
## More Specifically
To be a bit more specific, _physics_ is a huge field, and we can't cover everything...
```{note}
For now our focus are:
- _field-based simulations_ (no Lagrangian methods)
- combinations with _deep learning_ (plenty of other interesting ML techniques, but not here)
- experiments as _outlook_ (replace synthetic data with real)
```
It's also worth noting that we're starting to build the methods from some very
fundamental steps. Here are some considerations for skipping ahead to the later chapters.
```{admonition} You can skip ahead if...
:class: tip
@@ -138,6 +155,9 @@ A brief look at our _Notation_ won't hurt in both cases, though!
```
---
<br>
<br>
<br>
<!-- ## A brief history of PBDL in the context of Fluids
@@ -154,6 +174,8 @@ PINNs ... and more ... -->
## Deep Learning and Neural Networks
TODO
Very brief intro, basic equations... approximate $f^*(x)=y$ with NN $f(x;\theta)$ ...
learn via GD, $\partial f / \partial \theta$

4
physicalloss-code.ipynb
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@@ -18,7 +18,7 @@
"\n",
"## Preliminaries\n",
"\n",
"Let's just load TF for..."
"Let's just load TF and phiflow for now, and initialize the random sampling."
]
},
{
@@ -54,7 +54,7 @@
"from phi.tf.flow import *\n",
"import numpy as np\n",
"\n",
"#rnd = TF_BACKEND # sample different points in the domain each iteration\n",
"#rnd = TF_BACKEND # for phiflow: sample different points in the domain each iteration\n",
"rnd = math.choose_backend(1) # use same random points for all iterations"
]
},

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