480 lines
176 KiB
Plaintext
Vendored
480 lines
176 KiB
Plaintext
Vendored
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Tutorial: Multiscale PDE learning with Fourier Feature Network\n",
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"\n",
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"[](https://colab.research.google.com/github/mathLab/PINA/blob/master/tutorials/tutorial13/tutorial.ipynb)\n",
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"\n",
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"This tutorial presents how to solve with Physics-Informed Neural Networks (PINNs)\n",
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"a PDE characterized by multiscale behaviour, as\n",
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"presented in [*On the eigenvector bias of Fourier feature networks: From regression to solving\n",
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"multi-scale PDEs with physics-informed neural networks*](\n",
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"https://doi.org/10.1016/j.cma.2021.113938). \n",
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"\n",
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"First of all, some useful imports."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"## routine needed to run the notebook on Google Colab\n",
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"try:\n",
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" import google.colab\n",
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" IN_COLAB = True\n",
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"except:\n",
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" IN_COLAB = False\n",
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"if IN_COLAB:\n",
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" !pip install \"pina-mathlab\"\n",
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"\n",
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"import torch\n",
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"import matplotlib.pyplot as plt\n",
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"import warnings\n",
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"\n",
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"from pina import Condition, Trainer\n",
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"from pina.problem import SpatialProblem\n",
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"from pina.operator import laplacian\n",
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"from pina.solver import PINN, SelfAdaptivePINN as SAPINN\n",
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"from pina.model.block import FourierFeatureEmbedding\n",
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"from pina.loss import LpLoss\n",
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"from pina.domain import CartesianDomain\n",
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"from pina.equation import Equation, FixedValue\n",
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"from pina.model import FeedForward\n",
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"\n",
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"warnings.filterwarnings('ignore')"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Multiscale Problem\n",
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"\n",
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"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",
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"multi-scale PDEs with physics-informed neural networks*](\n",
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"https://doi.org/10.1016/j.cma.2021.113938). The one-dimensional Poisson problem we aim to solve is mathematically written as:\n",
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"\n",
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"\\begin{equation}\n",
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"\\begin{cases}\n",
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"\\Delta u (x) + f(x) = 0 \\quad x \\in [0,1], \\\\\n",
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"u(x) = 0 \\quad x \\in \\partial[0,1], \\\\\n",
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"\\end{cases}\n",
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"\\end{equation}\n",
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"\n",
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"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",
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"Though this example is simple and pedagogical, it is worth noting that\n",
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"the solution exhibits low frequency in the macro-scale and high frequency in the micro-scale, which resembles many\n",
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"practical scenarios.\n",
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"\n",
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"\n",
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"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."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"class Poisson(SpatialProblem):\n",
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" output_variables = ['u']\n",
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" spatial_domain = CartesianDomain({'x': [0, 1]})\n",
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"\n",
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" def poisson_equation(input_, output_):\n",
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" x = input_.extract('x')\n",
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" u_xx = laplacian(output_, input_, components=['u'], d=['x'])\n",
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" f = ((2*torch.pi)**2)*torch.sin(2*torch.pi*x) + 0.1*((50*torch.pi)**2)*torch.sin(50*torch.pi*x)\n",
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" return u_xx + f\n",
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"\n",
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" # here we write the problem conditions\n",
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" conditions = {\n",
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" 'bound_cond0' : Condition(domain=CartesianDomain({'x': 0.}),\n",
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" equation=FixedValue(0.)),\n",
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" 'bound_cond1' : Condition(domain=CartesianDomain({'x': 1.}),\n",
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" equation=FixedValue(0.)),\n",
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" 'phys_cond': Condition(domain=spatial_domain,\n",
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" equation=Equation(poisson_equation)),\n",
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" }\n",
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"\n",
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" def truth_solution(self, x):\n",
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" return torch.sin(2*torch.pi*x) + 0.1*torch.sin(50*torch.pi*x)\n",
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"\n",
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"problem = Poisson()\n",
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"\n",
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"# let's discretise the domain\n",
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"problem.discretise_domain(128, 'grid', domains=['phys_cond'])\n",
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"problem.discretise_domain(1, 'grid', domains=['bound_cond0','bound_cond1'])"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"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",
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"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",
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"\n",
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"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)."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"GPU available: False, used: False\n",
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"TPU available: False, using: 0 TPU cores\n",
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"HPU available: False, using: 0 HPUs\n"
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]
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Epoch 4999: 100%|██████████| 1/1 [00:00<00:00, 45.69it/s, v_num=71, bound_cond0_loss=2.38e+3, bound_cond1_loss=2.38e+3, phys_cond_loss=223.0, train_loss=4.99e+3] "
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]
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"`Trainer.fit` stopped: `max_epochs=5000` reached.\n"
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]
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Epoch 4999: 100%|██████████| 1/1 [00:00<00:00, 33.79it/s, v_num=71, bound_cond0_loss=2.38e+3, bound_cond1_loss=2.38e+3, phys_cond_loss=223.0, train_loss=4.99e+3]\n"
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]
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"GPU available: False, used: False\n",
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"TPU available: False, using: 0 TPU cores\n",
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"HPU available: False, using: 0 HPUs\n"
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]
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Epoch 4999: 100%|██████████| 1/1 [00:00<00:00, 13.96it/s, v_num=72, bound_cond0_loss=1.31e+3, bound_cond1_loss=1.45e+3, phys_cond_loss=75.70, train_loss=2.83e+3] "
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]
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"`Trainer.fit` stopped: `max_epochs=5000` reached.\n"
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]
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Epoch 4999: 100%|██████████| 1/1 [00:00<00:00, 11.95it/s, v_num=72, bound_cond0_loss=1.31e+3, bound_cond1_loss=1.45e+3, phys_cond_loss=75.70, train_loss=2.83e+3]\n"
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]
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}
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],
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"source": [
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"from pina.optim import TorchScheduler\n",
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"\n",
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"# training with PINN and visualize results\n",
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"model=FeedForward(input_dimensions=1, output_dimensions=1, layers=[100, 100, 100])\n",
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"pinn = PINN(problem=problem,\n",
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" model=model,\n",
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" scheduler=TorchScheduler(torch.optim.lr_scheduler.MultiStepLR, # Pass the class directly, not an instance\n",
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" milestones=[1000,2000,3000,4000],\n",
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" gamma=0.9))\n",
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"\n",
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"trainer = Trainer(pinn, max_epochs=5000, accelerator='cpu', enable_model_summary=False, val_size=0., train_size=1., test_size=0.)\n",
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"trainer.train()\n",
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"\n",
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"# training with PINN and visualize results\n",
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"sapinn = SAPINN(problem=problem,\n",
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" model=model,\n",
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" scheduler_model=TorchScheduler(torch.optim.lr_scheduler.MultiStepLR, \n",
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" milestones=[1000,2000,3000,4000],\n",
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" gamma=0.9))\n",
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"trainer_sapinn = Trainer(sapinn, max_epochs=5000, accelerator='cpu', enable_model_summary=False, val_size=0., train_size=1., test_size=0.)\n",
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"trainer_sapinn.train()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": 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",
|
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"text/plain": [
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"<Figure size 800x800 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
},
|
|
{
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"data": {
|
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"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 95.53%\n",
|
|
"Relative l2 error SAPINN 95.53%\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, 20.67it/s, v_num=73, bound_cond0_loss=7.38e-5, bound_cond1_loss=7.52e-5, phys_cond_loss=0.0209, train_loss=0.021] "
|
|
]
|
|
},
|
|
{
|
|
"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, 16.99it/s, v_num=73, bound_cond0_loss=7.38e-5, bound_cond1_loss=7.52e-5, phys_cond_loss=0.0209, train_loss=0.021]\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: 2.94%\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
|
|
}
|