Files
PINA/tutorials/tutorial13/tutorial.ipynb
Dario Coscia 29b14ee9b6 Update Tutorials (#544)
* update tutorials
* tutorial guidelines
* doc
2025-04-23 18:53:30 +02:00

513 lines
133 KiB
Plaintext
Vendored
Raw Permalink Blame History

This file contains ambiguous Unicode characters
This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Tutorial: Learning Multiscale PDEs Using Fourier Feature Networks\n",
"\n",
"[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/mathLab/PINA/blob/master/tutorials/tutorial13/tutorial.ipynb)\n",
"\n",
"This tutorial demonstrates how to solve a PDE with multiscale behavior using Physics-Informed Neural Networks (PINNs), as discussed in [*On the Eigenvector Bias of Fourier Feature Networks: From Regression to Solving Multi-Scale PDEs with Physics-Informed Neural Networks*](https://doi.org/10.1016/j.cma.2021.113938).\n",
"\n",
"Lets begin by importing the necessary libraries.\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"## routine needed to run the notebook on Google Colab\n",
"try:\n",
" import google.colab\n",
"\n",
" IN_COLAB = True\n",
"except:\n",
" IN_COLAB = False\n",
"if IN_COLAB:\n",
" !pip install \"pina-mathlab[tutorial]\"\n",
"\n",
"import torch\n",
"import matplotlib.pyplot as plt\n",
"import warnings\n",
"\n",
"from pina import Condition, Trainer\n",
"from pina.problem import SpatialProblem\n",
"from pina.operator import laplacian\n",
"from pina.solver import PINN, SelfAdaptivePINN as SAPINN\n",
"from pina.loss import LpLoss\n",
"from pina.domain import CartesianDomain\n",
"from pina.equation import Equation, FixedValue\n",
"from pina.model import FeedForward\n",
"from pina.model.block import FourierFeatureEmbedding\n",
"\n",
"warnings.filterwarnings(\"ignore\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Multiscale Problem\n",
"\n",
"We begin by presenting the problem, which is also discussed in Section 2 of [*On the Eigenvector Bias of Fourier Feature Networks: From Regression to Solving Multi-Scale PDEs with Physics-Informed Neural Networks*](https://doi.org/10.1016/j.cma.2021.113938). The one-dimensional Poisson problem we aim to solve is mathematically defined as:\n",
"\n",
"\\begin{equation}\n",
"\\begin{cases}\n",
"\\Delta u(x) + f(x) = 0 \\quad x \\in [0,1], \\\\\n",
"u(x) = 0 \\quad x \\in \\partial[0,1],\n",
"\\end{cases}\n",
"\\end{equation}\n",
"\n",
"We define the solution as:\n",
"\n",
"$$\n",
"u(x) = \\sin(2\\pi x) + 0.1 \\sin(50\\pi x),\n",
"$$\n",
"\n",
"which leads to the corresponding force term:\n",
"\n",
"$$\n",
"f(x) = (2\\pi)^2 \\sin(2\\pi x) + 0.1 (50 \\pi)^2 \\sin(50\\pi x).\n",
"$$\n",
"\n",
"While this example is simple and pedagogical, it's important to note that the solution exhibits low-frequency behavior in the macro-scale and high-frequency behavior in the micro-scale. This characteristic is common in many practical scenarios.\n",
"\n",
"Below is the implementation of the `Poisson` problem as described mathematically above.\n",
"> **👉 We have a dedicated [tutorial](https://mathlab.github.io/PINA/tutorial16/tutorial.html) to teach how to build a Problem from scratch — have a look if you're interested!**"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"class Poisson(SpatialProblem):\n",
" output_variables = [\"u\"]\n",
" spatial_domain = CartesianDomain({\"x\": [0, 1]})\n",
"\n",
" def poisson_equation(input_, output_):\n",
" x = input_.extract(\"x\")\n",
" u_xx = laplacian(output_, input_, components=[\"u\"], d=[\"x\"])\n",
" f = ((2 * torch.pi) ** 2) * torch.sin(2 * torch.pi * x) + 0.1 * (\n",
" (50 * torch.pi) ** 2\n",
" ) * torch.sin(50 * torch.pi * x)\n",
" return u_xx + f\n",
"\n",
" domains = {\n",
" \"bound_cond0\": CartesianDomain({\"x\": 0.0}),\n",
" \"bound_cond1\": CartesianDomain({\"x\": 1.0}),\n",
" \"phys_cond\": spatial_domain,\n",
" }\n",
" # here we write the problem conditions\n",
" conditions = {\n",
" \"bound_cond0\": Condition(\n",
" domain=\"bound_cond0\", equation=FixedValue(0.0)\n",
" ),\n",
" \"bound_cond1\": Condition(\n",
" domain=\"bound_cond1\", equation=FixedValue(0.0)\n",
" ),\n",
" \"phys_cond\": Condition(\n",
" domain=\"phys_cond\", equation=Equation(poisson_equation)\n",
" ),\n",
" }\n",
"\n",
" def solution(self, x):\n",
" return torch.sin(2 * torch.pi * x) + 0.1 * torch.sin(50 * torch.pi * x)\n",
"\n",
"\n",
"problem = Poisson()\n",
"\n",
"# let's discretise the domain\n",
"problem.discretise_domain(128, \"grid\", domains=[\"phys_cond\"])\n",
"problem.discretise_domain(1, \"grid\", domains=[\"bound_cond0\", \"bound_cond1\"])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A standard PINN approach would involve fitting the model using a Feed Forward (fully connected) Neural Network. For a conventional fully-connected neural network, it is relatively easy to approximate a function $u$, given sufficient data inside the computational domain. \n",
"\n",
"However, solving high-frequency or multi-scale problems presents significant challenges to PINNs, especially when the number of data points is insufficient to capture the different scales effectively.\n",
"\n",
"Below, we run a simulation using both the `PINN` solver and the self-adaptive `SAPINN` solver, employing a [`FeedForward`](https://mathlab.github.io/PINA/_modules/pina/model/feed_forward.html#FeedForward) model.\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"GPU available: True (mps), used: False\n",
"TPU available: False, using: 0 TPU cores\n",
"HPU available: False, using: 0 HPUs\n"
]
},
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "b9db39fafd844f7fa5e3cb0b39307330",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"Training: | | 0/? [00:00<?, ?it/s]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"`Trainer.fit` stopped: `max_epochs=1500` reached.\n",
"GPU available: True (mps), used: False\n",
"TPU available: False, using: 0 TPU cores\n",
"HPU available: False, using: 0 HPUs\n"
]
},
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "3e2af03ed4014a4ca0a2f4a6b96c10d1",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"Training: | | 0/? [00:00<?, ?it/s]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"`Trainer.fit` stopped: `max_epochs=1500` reached.\n"
]
}
],
"source": [
"# training with PINN and visualize results\n",
"pinn = PINN(\n",
" problem=problem,\n",
" model=FeedForward(\n",
" input_dimensions=1, output_dimensions=1, layers=[100, 100, 100]\n",
" ),\n",
")\n",
"\n",
"trainer = Trainer(\n",
" pinn,\n",
" max_epochs=1500,\n",
" accelerator=\"cpu\",\n",
" enable_model_summary=False,\n",
" val_size=0.0,\n",
" train_size=1.0,\n",
" test_size=0.0,\n",
")\n",
"trainer.train()\n",
"\n",
"# training with PINN and visualize results\n",
"sapinn = SAPINN(\n",
" problem=problem,\n",
" model=FeedForward(\n",
" input_dimensions=1, output_dimensions=1, layers=[100, 100, 100]\n",
" ),\n",
")\n",
"trainer_sapinn = Trainer(\n",
" sapinn,\n",
" max_epochs=1500,\n",
" accelerator=\"cpu\",\n",
" enable_model_summary=False,\n",
" val_size=0.0,\n",
" train_size=1.0,\n",
" test_size=0.0,\n",
")\n",
"trainer_sapinn.train()"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# define the function to plot the solution obtained using matplotlib\n",
"def plot_solution(pinn_to_use, title):\n",
" pts = pinn_to_use.problem.spatial_domain.sample(256, \"grid\", variables=\"x\")\n",
" predicted_output = pinn_to_use(pts).extract(\"u\").tensor.detach()\n",
" true_output = pinn_to_use.problem.solution(pts).detach()\n",
" plt.plot(\n",
" pts.extract([\"x\"]), predicted_output, label=\"Neural Network solution\"\n",
" )\n",
" plt.plot(pts.extract([\"x\"]), true_output, label=\"True solution\")\n",
" plt.title(title)\n",
" plt.legend()\n",
"\n",
"\n",
"# plot the solution of the two PINNs\n",
"plot_solution(pinn, \"PINN solution\")\n",
"plt.figure()\n",
"plot_solution(sapinn, \"Self Adaptive PINN solution\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can clearly observe that neither of the two solvers has successfully learned the solution. \n",
"The issue is not with the optimization strategy (i.e., the solver), but rather with the model used to solve the problem. \n",
"A simple `FeedForward` network struggles to handle multiscale problems, especially when there are not enough collocation points to capture the different scales effectively.\n",
"\n",
"Next, let's compute the $l_2$ relative error for both the `PINN` and `SAPINN` solutions:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Relative l2 error PINN 2593.94%\n",
"Relative l2 error SAPINN 1861.15%\n"
]
}
],
"source": [
"# l2 loss from PINA losses\n",
"l2_loss = LpLoss(p=2, relative=False)\n",
"\n",
"# sample new test points\n",
"pts = pts = problem.spatial_domain.sample(100, \"grid\")\n",
"print(\n",
" f\"Relative l2 error PINN {l2_loss(pinn(pts), problem.solution(pts)).item():.2%}\"\n",
")\n",
"print(\n",
" f\"Relative l2 error SAPINN {l2_loss(sapinn(pts), problem.solution(pts)).item():.2%}\"\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Which is indeed very high!\n",
"\n",
"## Fourier Feature Embedding in PINA\n",
"Fourier Feature Embedding is a technique used to transform the input features, aiding the network in learning multiscale variations in the output. It was first introduced in [*On the Eigenvector Bias of Fourier Feature Networks: From Regression to Solving Multi-Scale PDEs with Physics-Informed Neural Networks*](https://doi.org/10.1016/j.cma.2021.113938), where it demonstrated excellent results for multiscale problems.\n",
"\n",
"The core idea behind Fourier Feature Embedding is to map the input $\\mathbf{x}$ into an embedding $\\tilde{\\mathbf{x}}$, defined as:\n",
"\n",
"$$\n",
"\\tilde{\\mathbf{x}} = \\left[\\cos\\left( \\mathbf{B} \\mathbf{x} \\right), \\sin\\left( \\mathbf{B} \\mathbf{x} \\right)\\right],\n",
"$$\n",
"\n",
"where $\\mathbf{B}_{ij} \\sim \\mathcal{N}(0, \\sigma^2)$. This simple operation allows the network to learn across multiple scales!\n",
"\n",
"In **PINA**, we have already implemented this feature as a `layer` called [`FourierFeatureEmbedding`](https://mathlab.github.io/PINA/_rst/layers/fourier_embedding.html). Below, we will build the *Multi-scale Fourier Feature Architecture*. In this architecture, multiple Fourier feature embeddings (initialized with different $\\sigma$ values) are applied to the input coordinates. These embeddings are then passed through the same fully-connected neural network, and the outputs are concatenated with a final linear layer.\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"class MultiscaleFourierNet(torch.nn.Module):\n",
" def __init__(self):\n",
" super().__init__()\n",
" self.embedding1 = FourierFeatureEmbedding(\n",
" input_dimension=1, output_dimension=100, sigma=1\n",
" )\n",
" self.embedding2 = FourierFeatureEmbedding(\n",
" input_dimension=1, output_dimension=100, sigma=10\n",
" )\n",
" self.layers = FeedForward(\n",
" input_dimensions=100, output_dimensions=100, layers=[100]\n",
" )\n",
" self.final_layer = torch.nn.Linear(2 * 100, 1)\n",
"\n",
" def forward(self, x):\n",
" e1 = self.layers(self.embedding1(x))\n",
" e2 = self.layers(self.embedding2(x))\n",
" return self.final_layer(torch.cat([e1, e2], dim=-1))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will train the `MultiscaleFourierNet` using the `PINN` solver. \n",
"Feel free to experiment with other PINN variants as well, such as `SAPINN`, `GPINN`, `CompetitivePINN`, and others, to see how they perform on this multiscale problem."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"GPU available: True (mps), used: False\n",
"TPU available: False, using: 0 TPU cores\n",
"HPU available: False, using: 0 HPUs\n"
]
},
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "406bab5254d34c1dac9234243b2f3eb4",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"Training: | | 0/? [00:00<?, ?it/s]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"`Trainer.fit` stopped: `max_epochs=1500` reached.\n"
]
}
],
"source": [
"multiscale_pinn = PINN(problem=problem, model=MultiscaleFourierNet())\n",
"trainer = Trainer(\n",
" multiscale_pinn,\n",
" max_epochs=1500,\n",
" accelerator=\"cpu\",\n",
" enable_model_summary=False,\n",
" val_size=0.0,\n",
" train_size=1.0,\n",
" test_size=0.0,\n",
")\n",
"trainer.train()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us now plot the solution and compute the relative $l_2$ again!"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Relative l2 error PINN with MultiscaleFourierNet: 8.76%\n"
]
},
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# plot solution obtained\n",
"plot_solution(multiscale_pinn, \"Multiscale PINN solution\")\n",
"\n",
"# sample new test points\n",
"pts = pts = problem.spatial_domain.sample(100, \"grid\")\n",
"print(\n",
" f\"Relative l2 error PINN with MultiscaleFourierNet: {l2_loss(multiscale_pinn(pts), problem.solution(pts)).item():.2%}\"\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It is clear that the network has learned the correct solution, with a very low error. Of course, longer training and a more expressive neural network could further improve the results!\n",
"\n",
"## What's Next?\n",
"\n",
"Congratulations on completing the one-dimensional Poisson tutorial of **PINA** using `FourierFeatureEmbedding`! There are many potential next steps you can explore:\n",
"\n",
"1. **Train the network longer or with different layer sizes**: Experiment with different configurations to improve accuracy.\n",
"\n",
"2. **Understand the role of `sigma` in `FourierFeatureEmbedding`**: The original paper provides insightful details on the impact of `sigma`. It's a good next step to dive deeper into its effect.\n",
"\n",
"3. **Implement the *Spatio-temporal Multi-scale Fourier Feature Architecture***: Code this architecture for a more complex, time-dependent PDE (refer to Section 3 of the original paper).\n",
"\n",
"4. **...and many more!**: There are countless directions to further explore, from testing on different problems to refining the model architecture.\n",
"\n",
"For more resources and tutorials, check out the [PINA Documentation](https://mathlab.github.io/PINA/)."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "pina",
"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": "3.9.21"
}
},
"nbformat": 4,
"nbformat_minor": 2
}