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PINA/tutorials/tutorial13/tutorial.ipynb
2025-03-19 17:48:24 +01:00

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Tutorial: Multiscale PDE learning with Fourier Feature Network\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 presents how to solve with Physics-Informed Neural Networks (PINNs)\n",
"a PDE characterized by multiscale behaviour, as\n",
"presented in [*On the eigenvector bias of Fourier feature networks: From regression to solving\n",
"multi-scale PDEs with physics-informed neural networks*](\n",
"https://doi.org/10.1016/j.cma.2021.113938). \n",
"\n",
"First of all, some useful imports."
]
},
{
"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",
" IN_COLAB = True\n",
"except:\n",
" IN_COLAB = False\n",
"if IN_COLAB:\n",
" !pip install \"pina-mathlab\"\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.model.block import FourierFeatureEmbedding\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",
"\n",
"warnings.filterwarnings('ignore')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Multiscale Problem\n",
"\n",
"We begin by presenting the problem which also can be found in Section 2 of [*On the eigenvector bias of Fourier feature networks: From regression to solving\n",
"multi-scale PDEs with physics-informed neural networks*](\n",
"https://doi.org/10.1016/j.cma.2021.113938). The one-dimensional Poisson problem we aim to solve is mathematically written 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 impose the solution as $u(x) = \\sin(2\\pi x) + 0.1 \\sin(50\\pi x)$ and obtain the force term $f(x) = (2\\pi)^2 \\sin(2\\pi x) + 0.1 (50 \\pi)^2 \\sin(50\\pi x)$.\n",
"Though this example is simple and pedagogical, it is worth noting that\n",
"the solution exhibits low frequency in the macro-scale and high frequency in the micro-scale, which resembles many\n",
"practical scenarios.\n",
"\n",
"\n",
"In **PINA** this problem is written, as always, as a class [see here for a tutorial on the Problem class](https://mathlab.github.io/PINA/_rst/tutorials/tutorial1/tutorial.html). Below you can find the `Poisson` problem which is mathmatically described above."
]
},
{
"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*((50*torch.pi)**2)*torch.sin(50*torch.pi*x)\n",
" return u_xx + f\n",
"\n",
" # here we write the problem conditions\n",
" conditions = {\n",
" 'bound_cond0' : Condition(domain=CartesianDomain({'x': 0.}),\n",
" equation=FixedValue(0.)),\n",
" 'bound_cond1' : Condition(domain=CartesianDomain({'x': 1.}),\n",
" equation=FixedValue(0.)),\n",
" 'phys_cond': Condition(domain=spatial_domain,\n",
" equation=Equation(poisson_equation)),\n",
" }\n",
"\n",
" def truth_solution(self, x):\n",
" return torch.sin(2*torch.pi*x) + 0.1*torch.sin(50*torch.pi*x)\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 be to fit this model using a Feed Forward (fully connected) Neural Network. For a conventional fully-connected neural network is easy to\n",
"approximate a function $u$, given sufficient data inside the computational domain. However solving high-frequency or multi-scale problems presents great challenges to PINNs especially when the number of data cannot capture the different scales.\n",
"\n",
"Below we run a simulation using the `PINN` solver and the self adaptive `SAPINN` solver, using a [`FeedForward`](https://mathlab.github.io/PINA/_modules/pina/model/feed_forward.html#FeedForward) model. We used a `MultiStepLR` scheduler to decrease the learning rate slowly during training (it takes around 2 minutes to run on CPU)."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"GPU available: False, used: False\n",
"TPU available: False, using: 0 TPU cores\n",
"HPU available: False, using: 0 HPUs\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Epoch 4999: 100%|██████████| 1/1 [00:00<00:00, 53.24it/s, v_num=77, bound_cond0_loss=2.57e+3, bound_cond1_loss=2.57e+3, phys_cond_loss=421.0, train_loss=5.57e+3] "
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"`Trainer.fit` stopped: `max_epochs=5000` reached.\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Epoch 4999: 100%|██████████| 1/1 [00:00<00:00, 38.84it/s, v_num=77, bound_cond0_loss=2.57e+3, bound_cond1_loss=2.57e+3, phys_cond_loss=421.0, train_loss=5.57e+3]\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"GPU available: False, used: False\n",
"TPU available: False, using: 0 TPU cores\n",
"HPU available: False, using: 0 HPUs\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Epoch 4999: 100%|██████████| 1/1 [00:00<00:00, 32.13it/s, v_num=78, bound_cond0_loss=633.0, bound_cond1_loss=660.0, phys_cond_loss=2.57e+3, train_loss=3.86e+3] "
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"`Trainer.fit` stopped: `max_epochs=5000` reached.\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Epoch 4999: 100%|██████████| 1/1 [00:00<00:00, 26.83it/s, v_num=78, bound_cond0_loss=633.0, bound_cond1_loss=660.0, phys_cond_loss=2.57e+3, train_loss=3.86e+3]\n"
]
}
],
"source": [
"from pina.optim import TorchScheduler\n",
"\n",
"# training with PINN and visualize results\n",
"pinn = PINN(problem=problem,\n",
" model=FeedForward(input_dimensions=1, output_dimensions=1, layers=[100, 100, 100]),\n",
" scheduler=TorchScheduler(torch.optim.lr_scheduler.MultiStepLR, # Pass the class directly, not an instance\n",
" milestones=[1000,2000,3000,4000],\n",
" gamma=0.9))\n",
"\n",
"trainer = Trainer(pinn, max_epochs=5000, accelerator='cpu', enable_model_summary=False, val_size=0., train_size=1., test_size=0.)\n",
"trainer.train()\n",
"\n",
"# training with PINN and visualize results\n",
"sapinn = SAPINN(problem=problem,\n",
" model=FeedForward(input_dimensions=1, output_dimensions=1, layers=[100, 100, 100]),\n",
" scheduler_model=TorchScheduler(torch.optim.lr_scheduler.MultiStepLR, \n",
" milestones=[1000,2000,3000,4000],\n",
" gamma=0.9))\n",
"trainer_sapinn = Trainer(sapinn, max_epochs=5000, accelerator='cpu', enable_model_summary=False, val_size=0., train_size=1., test_size=0.)\n",
"trainer_sapinn.train()"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 800x800 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 800x800 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.forward(pts).extract('u').as_subclass(torch.Tensor).cpu().detach()\n",
" true_output = pinn_to_use.problem.truth_solution(pts).cpu().detach()\n",
" pts = pts.cpu()\n",
" fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(8, 8))\n",
" ax.plot(pts.extract(['x']), predicted_output, label='Neural Network solution')\n",
" ax.plot(pts.extract(['x']), true_output, label='True solution')\n",
" plt.title(title)\n",
" plt.legend()\n",
"\n",
"#plot the solution of the two PINNs\n",
"plot_solution(pinn, 'PINN solution')\n",
"plot_solution(sapinn, 'Self Adaptive PINN solution')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can clearly see that the solution has not been learned by the two different solvers. Indeed the big problem is not in the optimization strategy (i.e. the solver), but in the model used to solve the problem. A simple `FeedForward` network can hardly handle multiscales if not enough collocation points are used!\n",
"\n",
"We can also compute the $l_2$ relative error for the `PINN` and `SAPINN` solutions:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Relative l2 error PINN 95.74%\n",
"Relative l2 error SAPINN 95.71%\n"
]
}
],
"source": [
"# l2 loss from PINA losses\n",
"l2_loss = LpLoss(p=2, relative=True)\n",
"\n",
"# sample new test points\n",
"pts = pts = problem.spatial_domain.sample(100, 'grid')\n",
"print(f'Relative l2 error PINN {l2_loss(pinn(pts), problem.truth_solution(pts)).item():.2%}')\n",
"print(f'Relative l2 error SAPINN {l2_loss(sapinn(pts), problem.truth_solution(pts)).item():.2%}')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Which is indeed very high!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Fourier Feature Embedding in PINA"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Fourier Feature Embedding is a way to transform the input features, to help the network in learning multiscale variations in the output. It was\n",
"first introduced in [*On the eigenvector bias of Fourier feature networks: From regression to solving\n",
"multi-scale PDEs with physics-informed neural networks*](\n",
"https://doi.org/10.1016/j.cma.2021.113938) showing great results for multiscale problems. The basic idea is to map the input $\\mathbf{x}$ into an embedding $\\tilde{\\mathbf{x}}$ where:\n",
"\n",
"$$ \\tilde{\\mathbf{x}} =\\left[\\cos\\left( \\mathbf{B} \\mathbf{x} \\right), \\sin\\left( \\mathbf{B} \\mathbf{x} \\right)\\right] $$\n",
"\n",
"and $\\mathbf{B}_{ij} \\sim \\mathcal{N}(0, \\sigma^2)$. This simple operation allow the network to learn on multiple scales! \n",
"\n",
"In PINA we already have implemented the 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 $\\sigma$)\n",
"are applied to input coordinates and then passed through the same fully-connected neural network, before the outputs are finally concatenated with a linear layer."
]
},
{
"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(input_dimension=1, \n",
" output_dimension=100,\n",
" sigma=1)\n",
" self.embedding2 = FourierFeatureEmbedding(input_dimension=1, \n",
" output_dimension=100,\n",
" sigma=10)\n",
" self.layers = FeedForward(input_dimensions=100, output_dimensions=100, layers=[100])\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` with the `PINN` solver (and feel free to try also with our PINN variants (`SAPINN`, `GPINN`, `CompetitivePINN`, ...)."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"GPU available: False, used: False\n",
"TPU available: False, using: 0 TPU cores\n",
"HPU available: False, using: 0 HPUs\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Epoch 4999: 100%|██████████| 1/1 [00:00<00:00, 40.89it/s, v_num=79, bound_cond0_loss=0.000113, bound_cond1_loss=0.000103, phys_cond_loss=57.90, train_loss=57.90] "
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"`Trainer.fit` stopped: `max_epochs=5000` reached.\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Epoch 4999: 100%|██████████| 1/1 [00:00<00:00, 32.99it/s, v_num=79, bound_cond0_loss=0.000113, bound_cond1_loss=0.000103, phys_cond_loss=57.90, train_loss=57.90]\n"
]
}
],
"source": [
"multiscale_pinn = PINN(problem=problem,\n",
" model=MultiscaleFourierNet(),\n",
" scheduler=TorchScheduler(torch.optim.lr_scheduler.MultiStepLR, \n",
" milestones=[1000,2000,3000,4000],\n",
" gamma=0.9))\n",
"trainer = Trainer(multiscale_pinn, max_epochs=5000, accelerator='cpu', enable_model_summary=False, val_size=0., train_size=1., test_size=0.) # we train on CPU and avoid model summary at beginning of training (optional)\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: 3.52%\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 800x800 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(f'Relative l2 error PINN with MultiscaleFourierNet: {l2_loss(multiscale_pinn(pts), problem.truth_solution(pts)).item():.2%}')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It is pretty clear that the network has learned the correct solution, with also a very low error. Obviously a longer training and a more expressive neural network could improve the results!\n",
"\n",
"## What's next?\n",
"\n",
"Congratulations on completing the one dimensional Poisson tutorial of **PINA** using `FourierFeatureEmbedding`! There are multiple directions you can go now:\n",
"\n",
"1. Train the network for longer or with different layer sizes and assert the finaly accuracy\n",
"\n",
"2. Understand the role of `sigma` in `FourierFeatureEmbedding` (see original paper for a nice reference)\n",
"\n",
"3. Code the *Spatio-temporal multi-scale Fourier feature architecture* for a more complex time dependent PDE (section 3 of the original reference)\n",
"\n",
"4. Many more..."
]
}
],
"metadata": {
"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": "3.12.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}