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PINA/tutorials/tutorial9/tutorial.ipynb
Dario Coscia 29b14ee9b6 Update Tutorials (#544)
* update tutorials
* tutorial guidelines
* doc
2025-04-23 18:53:30 +02:00

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Tutorial: Applying Periodic Boundary Conditions in PINNs to solve the Helmotz Problem\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/tutorial9/tutorial.ipynb)\n",
"\n",
"This tutorial demonstrates how to solve a one-dimensional Helmholtz equation with periodic boundary conditions (PBC) using Physics-Informed Neural Networks (PINNs). \n",
"We will use standard PINN training, augmented with a periodic input expansion as introduced in [*An Experts Guide to Training Physics-Informed Neural Networks*](https://arxiv.org/abs/2308.08468).\n",
"\n",
"Let's start with some useful imports:\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.model import FeedForward\n",
"from pina.model.block import PeriodicBoundaryEmbedding # The PBC module\n",
"from pina.solver import PINN\n",
"from pina.domain import CartesianDomain\n",
"from pina.equation import Equation\n",
"from pina.callback import MetricTracker\n",
"\n",
"warnings.filterwarnings(\"ignore\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Problem Definition\n",
"\n",
"The one-dimensional Helmholtz problem is mathematically expressed as:\n",
"\n",
"$$\n",
"\\begin{cases}\n",
"\\frac{d^2}{dx^2}u(x) - \\lambda u(x) - f(x) &= 0 \\quad \\text{for } x \\in (0, 2) \\\\\n",
"u^{(m)}(x = 0) - u^{(m)}(x = 2) &= 0 \\quad \\text{for } m \\in \\{0, 1, \\dots\\}\n",
"\\end{cases}\n",
"$$\n",
"\n",
"In this case, we seek a solution that is $C^{\\infty}$ (infinitely differentiable) and periodic with period 2, over the infinite domain $x \\in (-\\infty, \\infty)$. \n",
"\n",
"A classical PINN approach would require enforcing periodic boundary conditions (PBC) for all derivatives—an infinite set of constraints—which is clearly infeasible.\n",
"\n",
"To address this, we adopt a strategy known as *coordinate augmentation*. In this approach, we apply a coordinate transformation $v(x)$ such that the transformed inputs naturally satisfy the periodicity condition:\n",
"\n",
"$$\n",
"u^{(m)}(x = 0) - u^{(m)}(x = 2) = 0 \\quad \\text{for } m \\in \\{0, 1, \\dots\\}\n",
"$$\n",
"\n",
"For demonstration purposes, we choose the specific parameters:\n",
"\n",
"- $\\lambda = -10\\pi^2$\n",
"- $f(x) = -6\\pi^2 \\sin(3\\pi x) \\cos(\\pi x)$\n",
"\n",
"These yield an analytical solution:\n",
"\n",
"$$\n",
"u(x) = \\sin(\\pi x) \\cos(3\\pi x)\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"def helmholtz_equation(input_, output_):\n",
" x = input_.extract(\"x\")\n",
" u_xx = laplacian(output_, input_, components=[\"u\"], d=[\"x\"])\n",
" f = (\n",
" -6.0\n",
" * torch.pi**2\n",
" * torch.sin(3 * torch.pi * x)\n",
" * torch.cos(torch.pi * x)\n",
" )\n",
" lambda_ = -10.0 * torch.pi**2\n",
" return u_xx - lambda_ * output_ - f\n",
"\n",
"\n",
"class Helmholtz(SpatialProblem):\n",
" output_variables = [\"u\"]\n",
" spatial_domain = CartesianDomain({\"x\": [0, 2]})\n",
"\n",
" # here we write the problem conditions\n",
" conditions = {\n",
" \"phys_cond\": Condition(\n",
" domain=spatial_domain, equation=Equation(helmholtz_equation)\n",
" ),\n",
" }\n",
"\n",
" def solution(self, pts):\n",
" return torch.sin(torch.pi * pts) * torch.cos(3.0 * torch.pi * pts)\n",
"\n",
"\n",
"problem = Helmholtz()\n",
"\n",
"# let's discretise the domain\n",
"problem.discretise_domain(200, \"grid\", domains=[\"phys_cond\"])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As usual, the Helmholtz problem is implemented in **PINA** as a class. The governing equations are defined as `conditions`, which must be satisfied within their respective domains. The `solution` represents the exact analytical solution, which will be used to evaluate the accuracy of the predicted solution.\n",
"\n",
"For selecting collocation points, we use Latin Hypercube Sampling (LHS), a common strategy for efficient space-filling in high-dimensional domains \n",
"\n",
"## Solving the Problem with a Periodic Network\n",
"\n",
"Any $\\mathcal{C}^{\\infty}$ periodic function $u : \\mathbb{R} \\rightarrow \\mathbb{R}$ with period $L \\in \\mathbb{N}$ \n",
"can be constructed by composing an arbitrary smooth function $f : \\mathbb{R}^n \\rightarrow \\mathbb{R}$ with a smooth, periodic mapping$v : \\mathbb{R} \\rightarrow \\mathbb{R}^n$ of the same period $L$. That is,\n",
"\n",
"$$\n",
"u(x) = f(v(x)).\n",
"$$\n",
"\n",
"This formulation is general and can be extended to arbitrary dimensions. \n",
"For more details, see [*A Method for Representing Periodic Functions and Enforcing Exactly Periodic Boundary Conditions with Deep Neural Networks*](https://arxiv.org/pdf/2007.07442).\n",
"\n",
"In our specific case, we define the periodic embedding as:\n",
"\n",
"$$\n",
"v(x) = \\left[1, \\cos\\left(\\frac{2\\pi}{L} x\\right), \\sin\\left(\\frac{2\\pi}{L} x\\right)\\right],\n",
"$$\n",
"\n",
"which constitutes the coordinate augmentation. The function $f(\\cdot)$ is approximated by a neural network $NN_{\\theta}(\\cdot)$, resulting in the approximate PINN solution:\n",
"\n",
"$$\n",
"u(x) \\approx u_{\\theta}(x) = NN_{\\theta}(v(x)).\n",
"$$\n",
"\n",
"In **PINA**, this is implemented using the `PeriodicBoundaryEmbedding` layer for $v(x)$, \n",
"paired with any `pina.model` to define the neural network $NN_{\\theta}$. \n",
"\n",
"Lets see how this is put into practice!\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# we encapsulate all modules in a torch.nn.Sequential container\n",
"model = torch.nn.Sequential(\n",
" PeriodicBoundaryEmbedding(input_dimension=1, periods=2),\n",
" FeedForward(\n",
" input_dimensions=3, # output of PeriodicBoundaryEmbedding = 3 * input_dimension\n",
" output_dimensions=1,\n",
" layers=[10, 10],\n",
" ),\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As simple as that!\n",
"\n",
"In higher dimensions, you can specify different periods for each coordinate using a dictionary. \n",
"For example, `periods = {'x': 2, 'y': 3, ...}` indicates a periodicity of 2 in the $x$ direction, \n",
"3 in the $y$ direction, and so on.\n",
"\n",
"We will now solve the problem using the usual `PINN` and `Trainer` classes. After training, we'll examine the losses using the `MetricTracker` callback from `pina.callback`."
]
},
{
"cell_type": "code",
"execution_count": 4,
"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": "89a9749dc755477aa6ed7b5aa4dc3698",
"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=5000` reached.\n"
]
}
],
"source": [
"solver = PINN(problem=problem, model=model)\n",
"trainer = Trainer(\n",
" solver,\n",
" max_epochs=5000,\n",
" accelerator=\"cpu\",\n",
" enable_model_summary=False,\n",
" callbacks=[MetricTracker()],\n",
")\n",
"trainer.train()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# plot loss\n",
"trainer_metrics = trainer.callbacks[0].metrics\n",
"plt.plot(\n",
" range(len(trainer_metrics[\"train_loss\"])), trainer_metrics[\"train_loss\"]\n",
")\n",
"# plotting\n",
"plt.xlabel(\"epoch\")\n",
"plt.ylabel(\"loss\")\n",
"plt.yscale(\"log\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We are going to plot the solution now!"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x30ed81af0>"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pts = solver.problem.spatial_domain.sample(256, \"grid\", variables=\"x\")\n",
"predicted_output = solver(pts).extract(\"u\").tensor.detach()\n",
"true_output = solver.problem.solution(pts)\n",
"plt.plot(pts.extract([\"x\"]), predicted_output, label=\"Neural Network solution\")\n",
"plt.plot(pts.extract([\"x\"]), true_output, label=\"True solution\")\n",
"plt.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Great, they overlap perfectly! This seems a good result, considering the simple neural network used to some this (complex) problem. We will now test the neural network on the domain $[-4, 4]$ without retraining. In principle the periodicity should be present since the $v$ function ensures the periodicity in $(-\\infty, \\infty)$."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
"<Figure size 1500x500 with 3 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# plotting solution\n",
"with torch.no_grad():\n",
" # Notice here we put [-4, 4]!!!\n",
" new_domain = CartesianDomain({\"x\": [0, 4]})\n",
" x = new_domain.sample(1000, mode=\"grid\")\n",
" fig, axes = plt.subplots(1, 3, figsize=(15, 5))\n",
" # Plot 1\n",
" axes[0].plot(x, problem.solution(x), label=r\"$u(x)$\", color=\"blue\")\n",
" axes[0].set_title(r\"True solution $u(x)$\")\n",
" axes[0].legend(loc=\"upper right\")\n",
" # Plot 2\n",
" axes[1].plot(x, solver(x), label=r\"$u_{\\theta}(x)$\", color=\"green\")\n",
" axes[1].set_title(r\"PINN solution $u_{\\theta}(x)$\")\n",
" axes[1].legend(loc=\"upper right\")\n",
" # Plot 3\n",
" diff = torch.abs(problem.solution(x) - solver(x))\n",
" axes[2].plot(x, diff, label=r\"$|u(x) - u_{\\theta}(x)|$\", color=\"red\")\n",
" axes[2].set_title(r\"Absolute difference $|u(x) - u_{\\theta}(x)|$\")\n",
" axes[2].legend(loc=\"upper right\")\n",
" # Adjust layout\n",
" plt.tight_layout()\n",
" # Show the plots\n",
" plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It's clear that the network successfully captures the periodicity of the solution, with the error also exhibiting a periodic pattern. Naturally, training for a longer duration or using a more expressive neural network could further improve the results.\n",
"## What's next?\n",
"\n",
"Congratulations on completing the one-dimensional Helmholtz tutorial with **PINA**! Here are a few directions you can explore next:\n",
"\n",
"1. **Train longer or with different architectures**: Experiment with extended training or modify the network's depth and width to evaluate improvements in accuracy.\n",
"\n",
"2. **Apply `PeriodicBoundaryEmbedding` to time-dependent problems**: Explore more complex scenarios such as spatiotemporal PDEs (see the official documentation for examples).\n",
"\n",
"3. **Try extra feature training**: Integrate additional physical or domain-specific features to guide the learning process more effectively.\n",
"\n",
"4. **...and many more!**: Extend to higher dimensions, test on other PDEs, or even develop custom embeddings tailored to your problem.\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
}