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PINA/tutorials/tutorial9/tutorial.ipynb
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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": 1,
"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": 18,
"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=[64, 64],\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": null,
"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": "6b8400d1e51c442790495b6da70f25a7",
"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": [
"solver = PINN(problem=problem, model=model)\n",
"trainer = Trainer(\n",
" solver,\n",
" max_epochs=2000,\n",
" accelerator=\"cpu\",\n",
" enable_model_summary=False,\n",
" callbacks=[MetricTracker()],\n",
")\n",
"trainer.train()"
]
},
{
"cell_type": "code",
"execution_count": 20,
"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": 21,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x31ab88040>"
]
},
"execution_count": 21,
"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": 22,
"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
}