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PINA/tutorials/tutorial14/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: Learning Bifurcating PDE Solutions with Physics-Informed Deep Ensembles\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/tutorial14/tutorial.ipynb)\n",
"\n",
"This tutorial demonstrates how to use the Deep Ensemble Physics Informed Network (DeepEnsemblePINN) to learn PDEs exhibiting bifurcating behavior, as discussed in [*Learning and Discovering Multiple Solutions Using Physics-Informed Neural Networks with Random Initialization and Deep Ensemble*](https://arxiv.org/abs/2503.06320).\n",
"\n",
"Lets begin by importing the necessary libraries."
]
},
{
"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 lightning.pytorch.callbacks import Callback\n",
"\n",
"from pina import Trainer, Condition, LabelTensor\n",
"from pina.solver import DeepEnsemblePINN\n",
"from pina.model import FeedForward\n",
"from pina.operator import laplacian\n",
"from pina.problem import TimeDependentProblem\n",
"from pina.domain import CartesianDomain\n",
"from pina.equation import Equation\n",
"from pina.optim import TorchOptimizer\n",
"\n",
"warnings.filterwarnings(\"ignore\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Deep Ensemble\n",
"\n",
"Deep Ensemble methods improve model performance by leveraging the diversity of predictions generated by multiple neural networks trained on the same problem. Each network in the ensemble is trained independently—typically with different weight initializations or even slight variations in the architecture or data sampling. By combining their outputs (e.g., via averaging or majority voting), ensembles reduce overfitting, increase robustness, and improve generalization.\n",
"\n",
"This approach allows the ensemble to capture different perspectives of the problem, leading to more accurate and reliable predictions.\n",
"\n",
"<p align=\"center\">\n",
" <img src=\"../static/deep_ensemble.png\" alt=\"PINA Workflow\" width=\"600\"/>\n",
"</p>\n",
"\n",
"The image above illustrates a Deep Ensemble setup, where multiple models attempt to predict the text from an image. While individual models may make errors (e.g., predicting \"PONY\" instead of \"PINA\"), combining their outputs—such as taking the majority vote—often leads to the correct result. This ensemble effect improves reliability by mitigating the impact of individual model biases.\n",
"\n",
"\n",
"## Deep Ensemble Physics-Informed Networks\n",
"\n",
"In the context of Physics-Informed Neural Networks (PINNs), Deep Ensembles help the network discover different branches or multiple solutions of a PDE that exhibits bifurcating behavior.\n",
"\n",
"By training a diverse set of models with different initializations, Deep Ensemble methods overcome the limitations of single-initialization models, which may converge to only one of the possible solutions. This approach is particularly useful when the solution space of the problem contains multiple valid physical states or behaviors.\n",
"\n",
"\n",
"## The Bratu Problem\n",
"\n",
"In this tutorial, we'll train a `DeepEnsemblePINN` solver to solve a bifurcating ODE known as the **Bratu problem**. The ODE is given by:\n",
"\n",
"$$\n",
"\\frac{d^2u}{dt^2} + \\lambda e^u = 0, \\quad t \\in (0, 1)\n",
"$$\n",
"\n",
"with boundary conditions:\n",
"\n",
"$$\n",
"u(0) = u(1) = 0,\n",
"$$\n",
"\n",
"where $\\lambda > 0$ is a scalar parameter. The analytical solutions to the 1D Bratu problem can be expressed as:\n",
"\n",
"$$\n",
"u(t, \\alpha) = 2 \\log\\left(\\frac{\\cosh(\\alpha)}{\\cosh(\\alpha(1 - 2t))}\\right),\n",
"$$\n",
"\n",
"where $\\alpha$ satisfies:\n",
"\n",
"$$\n",
"\\cosh(\\alpha) - 2\\sqrt{2}\\alpha = 0.\n",
"$$\n",
"\n",
"When $\\lambda < 3.513830719$, the equation admits two solutions $\\alpha_1$ and $\\alpha_2$, which correspond to two distinct solutions of the original ODE: $u_1$ and $u_2$.\n",
"\n",
"In this tutorial, we set $\\lambda = 1$, which leads to:\n",
"\n",
"- $\\alpha_1 \\approx 0.37929$\n",
"- $\\alpha_2 \\approx 2.73468$\n",
"\n",
"We first write the problem class, we do not write the boundary conditions as we will hard impose them.\n",
"\n",
"> **👉 We have a dedicated [tutorial](https://mathlab.github.io/PINA/tutorial16/tutorial.html) to teach how to build a Problem — have a look if you're interested!**\n",
"\n",
"> **👉 We have a dedicated [tutorial](https://mathlab.github.io/PINA/tutorial3/tutorial.html) to teach how to impose hard constraints — have a look if you're interested!**"
]
},
{
"cell_type": "code",
"execution_count": 80,
"metadata": {},
"outputs": [],
"source": [
"# define bratu equation\n",
"def bratu_eq(input_, output_):\n",
" u_tt = laplacian(output_=output_, input_=input_, components=[\"u\"], d=[\"t\"])\n",
" return u_tt + torch.exp(output_)\n",
"\n",
"# define true solution\n",
"def true_solution(x):\n",
" alpha1 = torch.tensor([0.37929])\n",
" alpha2 = torch.tensor([2.73468])\n",
" u1 = 2 * torch.log(torch.cosh(alpha1) / torch.cosh(alpha1 * (1 - 2 * x)))\n",
" u2 = 2 * torch.log(torch.cosh(alpha2) / torch.cosh(alpha2 * (1 - 2 * x)))\n",
" return u1, u2\n",
"\n",
"# build problem class\n",
"class BratuProblem(TimeDependentProblem):\n",
" output_variables = [\"u\"]\n",
" temporal_domain = CartesianDomain({\"t\": [0, 1]})\n",
" domains = {\n",
" \"interior\": CartesianDomain({\"t\": [0, 1]}),\n",
" }\n",
" conditions = {\n",
" \"interior\": Condition(domain=\"interior\", equation=Equation(bratu_eq))\n",
" }\n",
"\n",
"# define problem and discretise domain\n",
"problem = BratuProblem()\n",
"problem.discretise_domain(n=101, mode=\"grid\", domains=\"interior\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Defining the Deep Ensemble Models\n",
"\n",
"Now that the problem setup is complete, we move on to creating an **ensemble of models**. Each ensemble member will be a standard `FeedForward` neural network, wrapped inside a custom `Model` class.\n",
"\n",
"Each model's weights are initialized using a **normal distribution** with mean 0 and standard deviation 2. This random initialization is crucial to promote diversity across the ensemble members, allowing the models to converge to potentially different solutions of the PDE.\n",
"\n",
"The final ensemble is simply a **list of PyTorch models**, which we will later pass to the `DeepEnsemblePINN`"
]
},
{
"cell_type": "code",
"execution_count": 81,
"metadata": {},
"outputs": [],
"source": [
"# define a single model (ensemble member)\n",
"class Model(torch.nn.Module):\n",
" def __init__(self, *args, **kwargs):\n",
" super().__init__()\n",
" self.model = FeedForward(*args, **kwargs)\n",
" self.init_weights_gaussian()\n",
"\n",
" def forward(self, x):\n",
" return x * (1 - x) * self.model(x)\n",
"\n",
" def init_weights_gaussian(self):\n",
" for param in self.model.parameters():\n",
" if param.requires_grad:\n",
" torch.nn.init.normal_(param, mean=0.0, std=2.0)\n",
"\n",
"# define a list of models with different initializations\n",
"models = [Model(1, 1, inner_size=50, n_layers=2) for _ in range(10)]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's visualize the networks output before strated training"
]
},
{
"cell_type": "code",
"execution_count": 82,
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# plot solution\n",
"with torch.no_grad():\n",
" pts = problem.input_pts[\"interior\"]\n",
" for model in models:\n",
" plt.plot(pts, model(pts), \"--\")\n",
" plt.plot()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As you can see we get different output since the neural networks are initialized differently.\n",
"\n",
"## Training with `DeepEnsemblePINN`\n",
"\n",
"Now that everything is ready, we can train the models using the `DeepEnsemblePINN` solver! 🎯\n",
"\n",
"This solver is constructed by combining multiple neural network models that all aim to solve the same PDE. Each model $\\mathcal{M}_{i \\in \\{1, \\dots, 10\\}}$ in the ensemble contributes a unique perspective due to different random initializations.\n",
"\n",
"This diversity allows the ensemble to **capture multiple branches or bifurcating solutions** of the problem, making it especially powerful for PDEs like the Bratu problem.\n",
"\n",
"Once the `DeepEnsemblePINN` solver is defined with all the models, we train them using the `Trainer` class, as with any other solver in **PINA**. We also build a callback to store the value of `u(0.5)` during training iterations."
]
},
{
"cell_type": "code",
"execution_count": 83,
"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": "07f1c3ae122049edabaa0d0f2f5ccb02",
"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=500` reached.\n"
]
}
],
"source": [
"# define the optimizers, one per model\n",
"optimizers = [TorchOptimizer(torch.optim.Adam, lr=0.006) for _ in range(10)]\n",
"\n",
"# define solver\n",
"solver = DeepEnsemblePINN(\n",
" problem,\n",
" models,\n",
" optimizers=optimizers,\n",
")\n",
"\n",
"# callback\n",
"class StoreValue(Callback):\n",
" def on_train_epoch_start(self, trainer, pl_module):\n",
" input = LabelTensor(torch.tensor([[0.5]]), 't')\n",
" output = pl_module(input).tensor.flatten()\n",
" if trainer.current_epoch == 0:\n",
" self.store = [output]\n",
" else:\n",
" self.store.append(output)\n",
"\n",
"# define trainer\n",
"trainer = Trainer(\n",
" solver,\n",
" max_epochs=500,\n",
" accelerator=\"cpu\",\n",
" enable_model_summary=False,\n",
" callbacks=[StoreValue()],\n",
")\n",
"\n",
"# train\n",
"trainer.train()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The training finished, let's first plot how the value of $u(0.5)$ changed during training"
]
},
{
"cell_type": "code",
"execution_count": 84,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"with torch.no_grad():\n",
" metrics = torch.stack(trainer.callbacks[0].store, dim=0)\n",
" plt.plot(range(metrics.shape[0]), metrics)\n",
" plt.title('Ensemble Convergence')\n",
" plt.ylabel(r'$u(0.5)$')\n",
" plt.xlabel('epochs')\n",
" plt.plot()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As you can see, different networks in the ensemble converge to different values pf $u(0.5)$ — this means we can actually **spot the bifurcation** in the solution space!\n",
"\n",
"This is a powerful demonstration of how **Deep Ensemble Physics-Informed Neural Networks** are capable of learning **multiple valid solutions** of a PDE that exhibits bifurcating behavior.\n",
"\n",
"We can also visualize the ensemble predictions to better observe the multiple branches:\n"
]
},
{
"cell_type": "code",
"execution_count": 88,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# plot solution\n",
"with torch.no_grad():\n",
" pts = problem.input_pts[\"interior\"]\n",
" u_ensemble = solver(pts)\n",
" u1, u2 = true_solution(pts)\n",
" plt.plot(pts, u1, label=\"Reference solution u1\")\n",
" plt.plot(pts, u2, label=\"Reference solution u2\")\n",
" for idx, sol in enumerate(u_ensemble):\n",
" if idx == 0:\n",
" plt.plot(pts, sol, \"--\", label=\"PINNs\", c='k')\n",
" else:\n",
" plt.plot(pts, sol, \"--\", c=\"k\")\n",
" plt.legend()\n",
" plt.plot()\n",
" plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## What's Next?\n",
"\n",
"You have completed the tutorial on deep ensemble PINNs for bifurcating PDEs, well don! There are many potential next steps you can explore:\n",
"\n",
"1. **Train the network longer or with different hyperparameters**: Experiment with different configurations of the single model, you can compose an ensemble by also stacking models with different layers, activation, ... to improve accuracy.\n",
"\n",
"2. **Solve more complex problems**: The original paper provides very complex problems that can be solved with PINA, we suggest you to try implement and solve them!\n",
"\n",
"3. **...and many more!**: There are countless directions to further explore, for example, what does it happen when you vary the network initialization hyperparameters?\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
}