From 9bd9f531eadb4e73c408f90c048540d0a79872cc Mon Sep 17 00:00:00 2001 From: N_T Date: Fri, 25 Oct 2024 13:40:52 +0800 Subject: [PATCH] added HH learning code --- _toc.yml | 1 + physicalloss-div.ipynb | 893 +++++++++++++++++++++++++++++++++++++++++ physicalloss.md | 13 +- 3 files changed, 902 insertions(+), 5 deletions(-) create mode 100644 physicalloss-div.ipynb diff --git a/_toc.yml b/_toc.yml index 36a509b..13d096f 100644 --- a/_toc.yml +++ b/_toc.yml @@ -17,6 +17,7 @@ parts: - caption: Physical Losses chapters: - file: physicalloss.md + - file: physicalloss-div.ipynb - file: physicalloss-code.ipynb - file: physicalloss-discuss.md - caption: Differentiable Physics diff --git a/physicalloss-div.ipynb b/physicalloss-div.ipynb new file mode 100644 index 0000000..24ac4a3 --- /dev/null +++ b/physicalloss-div.ipynb @@ -0,0 +1,893 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "fiQvU0_fCXwj" + }, + "source": [ + "# Learning the Helmholtz-Hodge Decomposition\n", + "\n", + "In the following notebook we'll following the aforementioned paper by Tompson et al. {cite}`tompson2017` and train a neural network that can essentially perform a Helmholtz-Hodge decomposition. This is a very classic and time consuming part of many numerical solvers, and enables splitting an aribtrary vector field into a solenoidal (divergence-free) and irrotational part (the pressure gradient). Because this is traditionally veru time consuming, it's an interesting goal for a learned approach. As a stepping stone towards integrating full solvers, we'll formulate a physics-based loss via a discretized PDE-constraint.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "VF33GyuyCXwk" + }, + "source": [ + "## Solving Navier-Stokes\n", + "\n", + "To motivate the topic, let's briefly revisit how the incompressible Navier-Stokes equations are often solved: a fundamental variant employs operator splitting to separately solve advection and pressure correction (giving first-order accuracy in time). Thus, given an arbitrary flow field $\\mathbf{u}$, we compute a self advection step solving $\\frac{\\partial \\mathbf{u}}{\\partial{t}} + \\mathbf{u} \\cdot \\nabla \\mathbf{u} = 0$. This step is usually efficient, with a complexity linear in the number of discretization points, and gives an advected flow field $\\tilde{\\mathbf{u}}$. \n", + "\n", + "The pressure-projection (or _Chorin_ projection) step using the aforementioned Helmholtz-Hodge decomposition requires solving a Poisson problem $\\nabla ^ 2 p = \\nabla \\cdot \\tilde{\\mathbf{u}}$, an elliptic PDE that is non-trivial to solve in the general case. In the Navier-Stokes setting it gives an instantaneous scalar pressure field $p$, the gradient of which happens to capture the divergent parts of the velocity field. Hence, once we subtract $\\nabla p$ we obtain a divergence free field that satisfies $\\nabla \\cdot \\mathbf{u} = 0$." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "ikG8LK18CXwl" + }, + "source": [ + "Our goal below will be to obtain $p$ for new velocity inputs $\\mathbf{u}$, and the neat property of this problem is\n", + "that we can perform this training without a supervised setup. I.e., we don't have to precompute a large number of $(\\mathbf{u},p)$ pairs to train this, but rather we'll rely on the discretized PDE-constraint. This could be called an _unsupervised_ training, but this labeling is misleading, as the training target in all \"unsupervised\" cases is simply computed on the fly.\n", + "\n", + "The more important conceptual aspect of the approach is that we have a target PDE $\\nabla \\cdot \\mathbf{u} = 0$, that we can discretize on our computational domain with a suitable finite-difference operator. Once we do this in a differentiable way, we can directly use the FD operator to train our neural network: as we aim for minimizing $\\nabla \\cdot \\tilde{\\tilde{\\mathbf{u}}}$, this effectively gives us an $L_2$ loss with a target of 0. From this loss, we can back-propagate through the discretized divergence operator to obtain a gradient for $\\mathbf{u}$, which is computed (as outlined above), as $\\tilde{\\tilde{\\mathbf{u}}} = \\tilde{\\mathbf{u}} - \\nabla p$, where $p$ is the output of our neural network $f$ with parameters $\\theta$. \n", + "As we know that the divergence is all that is required to uniquely determine the pressure field, we can pass the divergence to $f$ to simplify the inference task.\n", + "Thus $f( \\nabla \\cdot \\tilde{\\mathbf{u}} ; \\theta)$ will receive a gradient backpropagated from the loss through all steps to update its state $\\theta$ such that the velocity field above will end up divergence free.\n", + "\n", + "Putting these steps together, we aim for solving the minimization problem\n", + "$$\n", + "\\text{arg min}_{\\theta} \\sum_i \\Big( \\nabla \\cdot (\\tilde{\\mathbf{u}} - \\nabla f(\\nabla \\cdot \\tilde{\\mathbf{u}} ; \\theta)) \\Big)^2 ,\n", + "$$\n", + "where the $i$ subscript denotes an arbitrary number of different inputs, e.g., from a minibatch at training time.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "KTZ4m8rnCXwl" + }, + "source": [ + "## Setting up the Discrete PDE\n", + "\n", + "As before, we'll use the `PhiFlow` framework. \n", + "The cell below installs it via `pip`, and imports the PyTorch backend together with `tqdm` for tracking the progress. Note that this notebook can be switched to TensorFlow quite easily by changing the import below." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "id": "EK8xTOQlCXwm" + }, + "outputs": [], + "source": [ + "!pip install --quiet phiflow==3.1 tqdm\n", + "from tqdm import tqdm\n", + "from phiml import nn\n", + "\n", + "from phi.torch.flow import *\n", + "# this notebook largely works identically with tensorflow - try replacing the line above with this one\n", + "#from phi.tf.flow import * " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "opKU6RVrCXwm" + }, + "source": [ + "Let's define some basic constants, the grid resolution (which we'll reuse as _physical_ dimensions in PhiFlow), the number of different flow fields we'll consider for training, and the batch size." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "id": "hs8v9vEECXwn" + }, + "outputs": [], + "source": [ + "RES_X = 32\n", + "RES_Y = 32\n", + "\n", + "NUM_SAMPLES_TRAIN = 100\n", + "BATCH_SIZE = 10" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "-6mIFTtQCXwn" + }, + "source": [ + "We will use random, periodic flow fields generated via PhiFlow's frequency-based synthesis. The next cell will prec-compute all these flow fields (100 in total), and visualize an example. Note, we're simply taking random, divergent flow fields here. We don't know what the correct divergence-free counterparts are." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 463 + }, + "id": "CDCkr16bCXwn", + "outputId": "43131d6b-83c0-438e-9790-b40120f3b427" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Initial L2 of divergence: \u001b[94m195.28241\u001b[0m, max=1.8969224691390991\n" + ] + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "vel = field.StaggeredGrid(\n", + " values=field.Noise(batch(batch=NUM_SAMPLES_TRAIN)),\n", + " extrapolation=math.extrapolation.PERIODIC,\n", + " bounds=geom.Box(x=RES_X, y=RES_Y), \n", + " resolution=math.spatial(x=RES_X, y=RES_Y),\n", + ")\n", + "\n", + "# plot the velocity field\n", + "plot = vis.plot({ \"velocity\": vel.batch[0], \"vel. magnitude\": math.vec_length(vel.batch[0].at_centers().values), \"divergence\": field.divergence(vel.batch[0]), })\n", + "\n", + "# for initial assessments, let's print the typical divergence of an input\n", + "print( f\"Initial L2 of divergence: {math.l2_loss(field.divergence(vel.batch[0]))}, max={field.divergence(vel.batch[0]).values.max}\" )" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "p2zXNACNCXwo" + }, + "source": [ + "Here you can see the flowlines together with velocity magnitudes and the divergence per cell. The latter is exactly what we're aiming for removing. This visualization shows that the divergence is smaller than the actual magnitude of the velocities, with an average of around 0.4, as indicated by the L2 output right above the images.\n", + "\n", + "Next, we will define a Navier-Stokes simulation step. Given our reduced setup without external forces or obstacles, it's very simple: a call to an advection function in PhiFlow, followed by `fluid.make_incompressible()` to invoke the Poisson solver. We'll directly annotate this function and the following ones for JIT compilation with `@jit_compile`. This is important for good performance on GPUs, but it makes debugging much harder. So when changing the code, it's highly recommended to remove them. The code will work just as well without, just slower. Once everything's running as it should, re-activate JIT compilation for the _real_ training runs. \n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "id": "HxhmDFPOCXwo" + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/thuerey/anaconda3/envs/torch24/lib/python3.12/site-packages/phiml/math/_optimize.py:631: UserWarning: Possible rank deficiency detected. Matrix might be singular which can lead to convergence problems. Please specify using Solve(rank_deficiency=...).\n", + " warnings.warn(\"Possible rank deficiency detected. Matrix might be singular which can lead to convergence problems. Please specify using Solve(rank_deficiency=...).\")\n", + "/home/thuerey/anaconda3/envs/torch24/lib/python3.12/site-packages/phiml/backend/torch/_torch_backend.py:800: UserWarning: Sparse CSR tensor support is in beta state. If you miss a functionality in the sparse tensor support, please submit a feature request to https://github.com/pytorch/pytorch/issues. (Triggered internally at ../aten/src/ATen/SparseCsrTensorImpl.cpp:53.)\n", + " return torch.sparse_csr_tensor(row_pointers, column_indices, values, shape, device=values.device)\n", + "/home/thuerey/anaconda3/envs/torch24/lib/python3.12/site-packages/phiml/math/_optimize.py:631: UserWarning: Possible rank deficiency detected. Matrix might be singular which can lead to convergence problems. Please specify using Solve(rank_deficiency=...).\n", + " warnings.warn(\"Possible rank deficiency detected. Matrix might be singular which can lead to convergence problems. Please specify using Solve(rank_deficiency=...).\")\n" + ] + } + ], + "source": [ + "@jit_compile\n", + "def step(v, dt = 1.0):\n", + " v = advect.mac_cormack(v, v, dt)\n", + " v, p = fluid.make_incompressible(v, [])\n", + " return v, p\n", + "\n", + "v,p = step(vel)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "QYJ3jdLeCXwo" + }, + "source": [ + "This cell directly runs the solver on our random velocity field from before. If you're curious, you can plot it via `vis.plot()`. However, as we've demonstrated in earlier chapters that PhiFlow's NS solver works, we'll focus on the NN training. Our goal below is to train the network without having to precompute many pressure examples with a function like `make_incompressible()` above. Instead, we'll use the differentiable divergence operator to set up our training.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "IQuy2EYpfqXp" + }, + "source": [ + "## Neural Network Training\n", + "\n", + "As NN architecture for an elliptic problem, an architecture with global communication is suitable. Below, we initialize a U-Net, but feel free to try the ResNet variant, which works less well due to its lack of a wide receptive field. (Given that property, it's doing surprisingly well.) As we're dealing with a periodic domain for simplicity, the NN likewise needs to be configured for periodic processing via `periodic=True`. It's input is a single channel (the divergence), and the output a very different content, the pressure. However, for the network this is likewise simply a single, scalar channel. The `filters=24` determine the total number of parameters. Feel free to increase this to improve accuracy (and reduce computational performance of the NN inference). This is the classic accuracy vs performance trade-off that NNs share with all classic numerical methods.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "n2gn4poGCXwp", + "outputId": "b3cbf653-3681-4ba1-d83e-efe853479fa3" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "UNet(\n", + " (inc): DoubleConv(\n", + " (double_conv): Sequential(\n", + " (0): Conv2d(1, 24, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), padding_mode=circular)\n", + " (1): Identity()\n", + " (2): ReLU()\n", + " (3): Conv2d(24, 24, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), padding_mode=circular)\n", + " (4): Identity()\n", + " (5): ReLU(inplace=True)\n", + " )\n", + " )\n", + " (down1): Down(\n", + " (maxpool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False)\n", + " (conv): ResNetBlock(\n", + " (sample_input): Identity()\n", + " (bn_sample): Identity()\n", + " (bn1): Identity()\n", + " (conv1): Conv2d(24, 24, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))\n", + " (bn2): Identity()\n", + " (conv2): Conv2d(24, 24, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))\n", + " )\n", + " )\n", + " (up1): Up(\n", + " (up): Upsample(scale_factor=2.0, mode='bilinear')\n", + " (conv): DoubleConv(\n", + " (double_conv): Sequential(\n", + " (0): Conv2d(48, 24, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), padding_mode=circular)\n", + " (1): Identity()\n", + " (2): ReLU()\n", + " (3): Conv2d(24, 24, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), padding_mode=circular)\n", + " (4): Identity()\n", + " (5): ReLU(inplace=True)\n", + " )\n", + " )\n", + " )\n", + " (down2): Down(\n", + " (maxpool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False)\n", + " (conv): ResNetBlock(\n", + " (sample_input): Identity()\n", + " (bn_sample): Identity()\n", + " (bn1): Identity()\n", + " (conv1): Conv2d(24, 24, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))\n", + " (bn2): Identity()\n", + " (conv2): Conv2d(24, 24, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))\n", + " )\n", + " )\n", + " (up2): Up(\n", + " (up): Upsample(scale_factor=2.0, mode='bilinear')\n", + " (conv): DoubleConv(\n", + " (double_conv): Sequential(\n", + " (0): Conv2d(48, 24, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), padding_mode=circular)\n", + " (1): Identity()\n", + " (2): ReLU()\n", + " (3): Conv2d(24, 24, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), padding_mode=circular)\n", + " (4): Identity()\n", + " (5): ReLU(inplace=True)\n", + " )\n", + " )\n", + " )\n", + " (down3): Down(\n", + " (maxpool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False)\n", + " (conv): ResNetBlock(\n", + " (sample_input): Identity()\n", + " (bn_sample): Identity()\n", + " (bn1): Identity()\n", + " (conv1): Conv2d(24, 24, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))\n", + " (bn2): Identity()\n", + " (conv2): Conv2d(24, 24, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))\n", + " )\n", + " )\n", + " (up3): Up(\n", + " (up): Upsample(scale_factor=2.0, mode='bilinear')\n", + " (conv): DoubleConv(\n", + " (double_conv): Sequential(\n", + " (0): Conv2d(48, 24, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), padding_mode=circular)\n", + " (1): Identity()\n", + " (2): ReLU()\n", + " (3): Conv2d(24, 24, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), padding_mode=circular)\n", + " (4): Identity()\n", + " (5): ReLU(inplace=True)\n", + " )\n", + " )\n", + " )\n", + " (outc): Conv2d(24, 1, kernel_size=(1, 1), stride=(1, 1))\n", + ")\n", + "Total number of trainable parameters: 83521\n" + ] + } + ], + "source": [ + "from phiml import nn \n", + "\n", + "network = nn.u_net(in_channels=1, out_channels=1, levels=4, periodic=True, batch_norm=False, in_spatial=(RES_X, RES_Y), filters=24)\n", + "\n", + "# uncomment this for an alternative architecture that could generalize to different resolutions\n", + "#network = nn.res_net(in_channels=1,out_channels=1,layers=[32,32,32])\n", + "\n", + "# print network and parameter summary\n", + "from phiml.backend import BACKENDS\n", + "if any([b.name == 'torch' for b in BACKENDS]):\n", + " print(network)\n", + " print(\"Total number of trainable parameters: \"+ str( sum(p.numel() for p in network.parameters()) ))\n", + "elif any([b.name == 'tf' for b in BACKENDS]):\n", + " network.summary() \n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "q8uvCyqsCXwp" + }, + "source": [ + "As can be seen here, the NN has around 83k trainable parameters.\n", + "\n", + "Next we can setup the training process: the `eval_nn()` function below takes a batch of flow fields, computes their divergence, and calls the NN with these inputs. The resulting scalar field is converted to a PhiFlow tensor and interpreted as a pressure field. Its gradient is subtracted from the input flow following Helmholtz-Hodge. Our goal is to make the resulting flow field `v` incompressible, i.e., it's divergence should be minimal.\n", + "\n", + "To achieve this goal, we'll define a loss function that computes the $L^2$ of the per-cell divergence `loss_div()`. For convenience, we'll also define a helper functions `loss_func` that will be used by PhiFlow. This function evaluates the NN for an input, and computes the resulting loss. PhiFlow will call this function and then make sure the gradient backpropagates from the single loss value through the discrete divergence operator to the weights of the NN. Note that in the incompressible setting we always remove the divergence present in the flow, and hence the time step does not play a role.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "id": "46wOU55hCXwp" + }, + "outputs": [], + "source": [ + "@jit_compile\n", + "def eval_nn(v):\n", + " nn_input = field.divergence(field=v, order=2)\n", + " p = math.native_call(network, nn_input.values)\n", + " p = field.CenteredGrid(\n", + " values=p,\n", + " extrapolation=math.extrapolation.PERIODIC, \n", + " bounds=geom.Box(x=RES_X, y=RES_Y),\n", + " resolution=spatial(x=RES_X, y=RES_Y),\n", + " )\n", + " grad_pres = field.spatial_gradient(p, boundary=math.extrapolation.PERIODIC, at=v.sampled_at) \n", + " v = v - grad_pres\n", + " return v, p\n", + "\n", + "# loss functions\n", + "\n", + "@jit_compile\n", + "def loss_div(v):\n", + " div = field.divergence(field=v,order=2)\n", + " div_sum = 2 * math.l2_loss(div)\n", + " return div_sum, div\n", + "\n", + "@jit_compile\n", + "def loss_func(v):\n", + " v, p = eval_nn(v)\n", + " loss, div = loss_div(v) \n", + " return math.mean(loss,dim=batch), v, p" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "nymq_eSDCXwp" + }, + "source": [ + "Before training the network, let's look at what a randomly initialized network produces. Below we evaluate the untrained network on the first flow field input:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 551 + }, + "id": "wa9T3aXqCXwp", + "outputId": "b17a0492-7746-4dbe-ab3a-b3a59912fa03" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Loss for untrained network: \u001b[94m390.21857\u001b[0m\n" + ] + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "vel_untrained, pres_untrained = eval_nn(vel.batch[0])\n", + "\n", + "# optionally, visualize the outputs: this doesnt look much different from before as the NN is untrained\n", + "#plot = vis.plot( {\"vel untrained\": vel_untrained.batch[0], \"vel len. untrained\": math.vec_length(vel_untrained.batch[0].at_centers().values), \"div. untrained\": field.divergence(vel_untrained.batch[0]), })\n", + "\n", + "# print the loss and divergence sum of the corrected velocity from untrained NN\n", + "loss, div_untrained = loss_div(vel_untrained)\n", + "print(f\"Loss for untrained network: {loss}\")\n", + "\n", + "# also, we visualize the pressure field\n", + "plot = vis.plot(pres_untrained.batch[0],title=\"pres. untrained\")" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "ZNEQUTu_CXwq" + }, + "source": [ + "Not surprisingly, the pressure field looks quite random, and the loss in terms of divergence is large." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Zf2iFVn8gZ6K" + }, + "source": [ + "## Training\n", + "\n", + "With our setup so far, training is very simple: we simply choose a few of the random flow fields, and evaulate the network, and change its weights so that the divergence loss becomes smaller. We simply loop over our precomputed flow fields without randomization below for a fixed number of epochs. Our network converges surprisingly fast. After a few epochs the loss should have decreased by more than two orders of magnitude." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "D7Ip2Da3CXwq", + "outputId": "5b056c46-266b-4068-d207-1538a244d6e1" + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + " 0%| | 0/15 [00:00" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "vel_nn, p_nn = eval_nn(vel_test)\n", + "vel_solver, p_solver = fluid.make_incompressible(vel_test, [])\n", + "\n", + "loss, div = loss_div(vel_test)\n", + "print(f\"Original, mean divergence={loss.mean:.3f}, div. max={math.max(div.values).mean:.3f}\")\n", + "\n", + "loss, div = loss_div(vel_nn)\n", + "print(f\"NN, mean divergence={loss.mean:.3f}, div. max={math.max(div.values).mean:.3f}\")\n", + "\n", + "loss, div = loss_div(vel_solver)\n", + "print(f\"Solver, mean divergence={loss.mean:.3f}, div. max={math.max(div.values).mean:.3f}\")\n", + "\n", + "plot = vis.plot({ \"vel.\": vel_test.batch[0], \"vel. NN\": vel_nn.batch[0], \"vel. solver\": vel_solver.batch[0] })\n", + "plot = vis.plot({ \"div.\": field.divergence(vel_test.batch[0]), \"div. NN\": field.divergence(vel_nn.batch[0]), \"div. solver\": field.divergence(vel_solver.batch[0]), })" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "THe quantative evalation confirms that our network has learned to reduce the divergence. The remaining one is larger than the one from PhiFlow's solver, but nonetheless orders of magnitude smaller than the original one. The images at the bottom nicely visualize this.\n", + "\n", + "Next, let's check what pressure field the network has actually learned to produce." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 541 + }, + "id": "lAA8BKXrCXwr", + "outputId": "7eedc994-e28b-4cbf-8c36-231add1377fd" + }, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# plot the pressure on the training data, compared with the pressure given by traditional solver.\n", + "plot = vis.plot({\"pres. solver\": p_solver.batch[0], \"pres. NN\": p_nn.batch[0]}, same_scale=False)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "xJP_D4ruCXws" + }, + "source": [ + "Interestingly, these fields share some similarities in terms of their structures, but are clearly not identical. Also, they typically have strongly varying magnitudes (the NN training is stochastic, so the differences can vary). Often, the NN learns to generate values that are 10 times larger, while PhiFlows pressure solvers is constrained to produce values with a zero mean.\n", + "\n", + "Nonetheless, as measured above, the pressure field of the network successfully removes most of the divergence, and mathematically, the Poisson problem here has a null-space in the form of a constant offset: the offset does not play a role once we take the derivatives, and hence all offsets are perfectly valid solutions. Our differentiable loss used for training does not have any constraint on absolute values, and hence the network is free to use any offset it happens to produce from its random initialization." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "bwOdfQABZTOi" + }, + "source": [ + "## Tougher Tests: Fluid Simulations with Obstacles\n", + "\n", + "Our initial goal were Navier-Stokes solvers, and hence it's import to check whether our network can actually cope with inputs in the form of flow fields produced by a fluid solver. After all, it was only trained on the synthetic, randomized fields that are quite different from the motions of fluids. To make things more interesting, we'll directly include a buoyant smoke plume to drive the simulation, and an obstacle. \n", + "\n", + "The next cell sets up a simple domain with a smoke source and a square obstacle right above it." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "id": "JlcMjRduZPh4" + }, + "outputs": [], + "source": [ + "smoke = CenteredGrid(0, extrapolation.PERIODIC, x=RES_X, y=RES_Y, bounds=Box(x=RES_X, y=RES_Y)) \n", + "vel_smk = StaggeredGrid(0, extrapolation.PERIODIC, x=RES_X, y=RES_Y, bounds=Box(x=RES_X, y=RES_Y)) \n", + "\n", + "RECTANGLE = Obstacle(Box(x=(12, 20), y=(18, 20)))\n", + "INFLOW_LOCATION = tensor((16, 5), channel(vector='x,y'))\n", + "INFLOW = 0.6 * CenteredGrid(Sphere(center=INFLOW_LOCATION, radius=3), extrapolation.PERIODIC, x=RES_X, y=RES_Y, bounds=Box(x=RES_X, y=RES_Y))\n", + "CYLINDER = Obstacle(geom.infinite_cylinder(x=16, y=20, radius=3, inf_dim=None))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "4CpNw9lZhiXI" + }, + "source": [ + "In our NN-supported solver, we now have some options regarding how to impose the zero-velocity boundary conditions for the obstacle. The safest way to handle them is to set velocities both before and after invoking the NN-based pressure correction step. The former ensure the network sees the solid obstacle, and the second one ensures the boundaries are fulfilled even if the network has made slight errors at the obstacle boundary. Hence, we'll call PhiFlow's `apply_boundary_conditions()` two times in the `step_nn()` function below.\n", + "\n", + "In parallel, we'll also define a `step_obs()` function that runs a classic flow solver without NN for comparison." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "id": "-uiB8iYZCXwx" + }, + "outputs": [], + "source": [ + "dt = 0.1\n", + "\n", + "@jit_compile\n", + "def step_nn(v, dt, f, obstacle):\n", + " v = v + f * dt\n", + " v = advect.mac_cormack(v, v, dt)\n", + " v = fluid.apply_boundary_conditions(v, obstacle)\n", + " nn_input = field.divergence(field=v, order=2)\n", + " p = math.native_call(network, nn_input.values)\n", + "\n", + " p = field.CenteredGrid( values=p,\n", + " extrapolation=math.extrapolation.PERIODIC,\n", + " bounds=geom.Box(x=RES_X, y=RES_Y),\n", + " resolution=spatial(x=RES_X, y=RES_Y),\n", + " )\n", + " grad_pres = field.spatial_gradient(p, at=v.sampled_at) \n", + " v = v - grad_pres\n", + " v = fluid.apply_boundary_conditions(v, obstacle)\n", + " return v, p\n", + "\n", + "@jit_compile\n", + "def step_obs(v, dt, f, obstacle):\n", + " v = v + f * dt\n", + " v = advect.mac_cormack(v, v, dt)\n", + " v, p = fluid.make_incompressible(v, obstacle)\n", + " return v, p" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "k3FfUh61Z1d0" + }, + "source": [ + "Now we're ready to run and compare the simulations. The code below does this for `STEPS` simulation steps, running both solvers one after the other. The advected marker densities are tracked in the `traj_smk_X` lists, and allow for an intuitive, qualitative check regarding the results. The marker density is both driving and following the flow velocity, and thus nicely highlights changes in the motion of the simulated fluid." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 626 + }, + "id": "6_5wdcNUCXwx", + "outputId": "49a9b5d7-e9cf-40ac-f7af-77f4152968d8" + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + " 0%| | 0/50 [00:00" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "STEPS = 50\n", + "smk_solv = smoke\n", + "smk_nn = smoke\n", + "vel_smk_solv = vel_smk\n", + "vel_smk_nn = vel_smk\n", + "traj_smk_solv = [smk_solv]\n", + "traj_smk_nn = [smk_nn]\n", + "\n", + "# flexible backends require a small workaround for PyTorch's no_grad context here; by default (eg for TF) use a null-context\n", + "from contextlib import nullcontext \n", + "context = nullcontext() \n", + "if any([b.name == 'torch' for b in BACKENDS]):\n", + " context = torch.no_grad()\n", + "\n", + "with context:\n", + " for i in tqdm(range(STEPS)):\n", + " smk_solv = advect.mac_cormack(smk_solv, vel_smk_solv, dt=dt) + INFLOW\n", + " smk_nn = advect.mac_cormack(smk_nn, vel_smk_nn, dt=dt) + INFLOW\n", + " \n", + " buoyancy_force_solv = smk_solv * (0, 1.0) @ vel_smk_solv\n", + " buoyancy_force_nn = smk_nn * (0, 1.0) @ vel_smk_nn\n", + " \n", + " vel_smk_solv, _ = step_obs(vel_smk_solv, dt, buoyancy_force_solv, [RECTANGLE])\n", + " vel_smk_nn, _ = step_nn(vel_smk_nn, dt, buoyancy_force_nn, [RECTANGLE])\n", + " \n", + " traj_smk_solv.append(smk_solv)\n", + " traj_smk_nn.append(smk_nn)\n", + "\n", + "traj_smk_solv = field.stack(traj_smk_solv, batch('time'))\n", + "traj_smk_nn = field.stack(traj_smk_nn, batch('time'))\n", + "\n", + "plot = vis.plot({\"Solver\": traj_smk_solv.time[STEPS-1], \"NN\": traj_smk_nn.time[STEPS-1]}) # show last frame" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "dnd8eqT9iRXO" + }, + "source": [ + "The plot above shows the last frame of the simulations, and they're remarkably simiar. This results shows that the NN has successfully learned to reduce the divergence of arbitrary flows, despite having only seen the synthetic noisy inputs at training time.\n", + "\n", + "Moreover, it highlights the success of the differentiable discrete operator used for training. The training converges very quickly, and the trained network generalizaes in a _zero-shot_ fashion to completely new inputs. The network hasn't even seen any obstcles at training time, and can still infer (mostly correct) pressure fields to handle them. This aspect is nonetheless an interesting point for improvements of this implementation. The NN could receive the obstacle geometry as an additional input, and could be trained to pay special attention to the boundary region via increased loss values.\n", + "\n", + "Lastly, if you're interested in watching the full evolution of the simulated trajectories, you can comment out and run the following cell. It generates a movie that can be watched in the browser via PhiFlow's `plot(...,animate=X)` function." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#vis.plot({\"solver\": traj_smk_solv, \"nn\": traj_smk_nn}, animate='time') # uncomment to view animation" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "vrfGtqwGkoML" + }, + "source": [ + "# Next Steps\n", + "\n", + "- Improve the architecture of the neural network to boost its performance; obvious aspects to improve on are depth and features per layer, but other architectures are likewise worth a try.\n", + "- Especially fully convolutional architectures like the `res_net` above are worth a try: evaluate how well a trained NN with these architectures can handle new and larger input grids.\n", + "- Add support for obstacles with an additional input and an updated training data set.\n", + "\n" + ] + } + ], + "metadata": { + "accelerator": "GPU", + "colab": { + "gpuType": "A100", + "machine_shape": "hm", + "provenance": [] + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "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": "3.12.4" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/physicalloss.md b/physicalloss.md index 406565a..0675e02 100644 --- a/physicalloss.md +++ b/physicalloss.md @@ -109,7 +109,6 @@ in {doc}`diffphys` and after, we'll focus on direct NN representations (variant The second variant of employing physical residuals as soft constraints instead uses fully connected NNs to represent $\mathbf{u}$. This _physics-informed_ approach was popularized by Raissi et al. {cite}`raissi2019pinn`, and has some interesting pros and cons that we'll outline in the following. We will target this physics-informed version (variant 2) in the following code examples and discussions. - The central idea here is that the aforementioned general function $f$ that we're after in our learning problems can also be used to obtain a representation of a physical field, e.g., a field $\mathbf{u}$ that satisfies $R=0$. This means $\mathbf{u}(\mathbf{x})$ will be turned into $\mathbf{u}(\mathbf{x}, \theta)$ where we choose the NN parameters $\theta$ such that a desired $\mathbf{u}$ is @@ -144,9 +143,13 @@ For higher order derivatives, such as $\frac{\partial^2 u}{\partial x^2}$, we ca ## Summary so far -The approach above gives us a method to include physical equations into DL learning as a soft constraint: the residual loss. +The v2 approach above gives us a method to include physical equations into DL learning as a soft constraint: the residual loss. Typically, this setup is suitable for _inverse problems_, where we have certain measurements or observations -for which we want to find a PDE solution. Because of the high cost of the reconstruction (to be -demonstrated in the following), the solution manifold shouldn't be overly complex. E.g., it is typically not possible -to capture a wide range of solutions, such as with the previous supervised airfoil example, by only using a physical residual loss. +for which we want to find a PDE solution. Because of the ill-posedness of the optimization and learning problem, +and the high cost of the reconstruction (to be +demonstrated in the following), the solution manifold shouldn't be overly complex for these PINN approaches. +E.g., it is typically very involved to capture a wide range of solutions, such as with the previous supervised airfoil example. + +Next, we'll demonstrate these concepts with code: first, we'll show how learning the Helmholtz decomposition works out in +practice with a v1-approach. Afterwards, we'll illustrate the PINN-approaches with a practical example.