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PINA/tutorials/tutorial2/tutorial.ipynb
Nicola Demo 0c8072274e Tutorials and Doc (#191)
* Tutorial doc update
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Co-authored-by: Dario Coscia <dcoscia@euclide.maths.sissa.it>
Co-authored-by: Dario Coscia <dariocoscia@Dario-Coscia.local>
2023-11-17 09:51:29 +01:00

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{
"cells": [
{
"cell_type": "markdown",
"id": "de19422d",
"metadata": {},
"source": [
"# Tutorial: Two dimensional Poisson problem using Extra Features Learning\n",
"\n",
"This tutorial presents how to solve with Physics-Informed Neural Networks (PINNs) a 2D Poisson problem with Dirichlet boundary conditions. We will train with standard PINN's training, and with extrafeatures. For more insights on extrafeature learning please read [*An extended physics informed neural network for preliminary analysis of parametric optimal control problems*](https://www.sciencedirect.com/science/article/abs/pii/S0898122123002018).\n",
"\n",
"First of all, some useful imports."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "ad0b8dd7",
"metadata": {},
"outputs": [],
"source": [
"import torch\n",
"from torch.nn import Softplus\n",
"\n",
"from pina.problem import SpatialProblem\n",
"from pina.operators import laplacian\n",
"from pina.model import FeedForward\n",
"from pina.solvers import PINN\n",
"from pina.trainer import Trainer\n",
"from pina.plotter import Plotter\n",
"from pina.geometry import CartesianDomain\n",
"from pina.equation import Equation, FixedValue\n",
"from pina import Condition, LabelTensor\n",
"from pina.callbacks import MetricTracker"
]
},
{
"cell_type": "markdown",
"id": "492a37b4",
"metadata": {},
"source": [
"## The problem definition"
]
},
{
"cell_type": "markdown",
"id": "2c0b1777",
"metadata": {},
"source": [
"The two-dimensional Poisson problem is mathematically written as:\n",
"\\begin{equation}\n",
"\\begin{cases}\n",
"\\Delta u = \\sin{(\\pi x)} \\sin{(\\pi y)} \\text{ in } D, \\\\\n",
"u = 0 \\text{ on } \\Gamma_1 \\cup \\Gamma_2 \\cup \\Gamma_3 \\cup \\Gamma_4,\n",
"\\end{cases}\n",
"\\end{equation}\n",
"where $D$ is a square domain $[0,1]^2$, and $\\Gamma_i$, with $i=1,...,4$, are the boundaries of the square.\n",
"\n",
"The Poisson problem is written in **PINA** code as a class. The equations are written as *conditions* that should be satisfied in the corresponding domains. The *truth_solution*\n",
"is the exact solution which will be compared with the predicted one."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "82c24040",
"metadata": {},
"outputs": [],
"source": [
"class Poisson(SpatialProblem):\n",
" output_variables = ['u']\n",
" spatial_domain = CartesianDomain({'x': [0, 1], 'y': [0, 1]})\n",
"\n",
" def laplace_equation(input_, output_):\n",
" force_term = (torch.sin(input_.extract(['x'])*torch.pi) *\n",
" torch.sin(input_.extract(['y'])*torch.pi))\n",
" laplacian_u = laplacian(output_, input_, components=['u'], d=['x', 'y'])\n",
" return laplacian_u - force_term\n",
"\n",
" # here we write the problem conditions\n",
" conditions = {\n",
" 'gamma1': Condition(location=CartesianDomain({'x': [0, 1], 'y': 1}), equation=FixedValue(0.)),\n",
" 'gamma2': Condition(location=CartesianDomain({'x': [0, 1], 'y': 0}), equation=FixedValue(0.)),\n",
" 'gamma3': Condition(location=CartesianDomain({'x': 1, 'y': [0, 1]}), equation=FixedValue(0.)),\n",
" 'gamma4': Condition(location=CartesianDomain({'x': 0, 'y': [0, 1]}), equation=FixedValue(0.)),\n",
" 'D': Condition(location=CartesianDomain({'x': [0, 1], 'y': [0, 1]}), equation=Equation(laplace_equation)),\n",
" }\n",
"\n",
" def poisson_sol(self, pts):\n",
" return -(\n",
" torch.sin(pts.extract(['x'])*torch.pi)*\n",
" torch.sin(pts.extract(['y'])*torch.pi)\n",
" )/(2*torch.pi**2)\n",
" \n",
" truth_solution = poisson_sol\n",
"\n",
"problem = Poisson()\n",
"\n",
"# let's discretise the domain\n",
"problem.discretise_domain(25, 'grid', locations=['D'])\n",
"problem.discretise_domain(25, 'grid', locations=['gamma1', 'gamma2', 'gamma3', 'gamma4'])"
]
},
{
"cell_type": "markdown",
"id": "7086c64d",
"metadata": {},
"source": [
"## Solving the problem with standard PINNs"
]
},
{
"cell_type": "markdown",
"id": "72ba4501",
"metadata": {},
"source": [
"After the problem, the feed-forward neural network is defined, through the class `FeedForward`. This neural network takes as input the coordinates (in this case $x$ and $y$) and provides the unkwown field of the Poisson problem. The residual of the equations are evaluated at several sampling points (which the user can manipulate using the method `CartesianDomain_pts`) and the loss minimized by the neural network is the sum of the residuals.\n",
"\n",
"In this tutorial, the neural network is composed by two hidden layers of 10 neurons each, and it is trained for 1000 epochs with a learning rate of 0.006 and $l_2$ weight regularization set to $10^{-7}$. These parameters can be modified as desired. We use the `MetricTracker` class to track the metrics during training."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "e7d20d6d",
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/u/d/dcoscia/.local/lib/python3.9/site-packages/torch/cuda/__init__.py:546: UserWarning: Can't initialize NVML\n",
" warnings.warn(\"Can't initialize NVML\")\n",
"/u/d/dcoscia/.local/lib/python3.9/site-packages/torch/cuda/__init__.py:651: UserWarning: CUDA initialization: CUDA unknown error - this may be due to an incorrectly set up environment, e.g. changing env variable CUDA_VISIBLE_DEVICES after program start. Setting the available devices to be zero. (Triggered internally at ../c10/cuda/CUDAFunctions.cpp:109.)\n",
" return torch._C._cuda_getDeviceCount() if nvml_count < 0 else nvml_count\n",
"GPU available: False, used: False\n",
"TPU available: False, using: 0 TPU cores\n",
"IPU available: False, using: 0 IPUs\n",
"HPU available: False, using: 0 HPUs\n",
"Missing logger folder: /u/d/dcoscia/PINA/tutorials/tutorial2/lightning_logs\n"
]
},
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "ad89e036986b443d912ab0dd6e427250",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"Training: 0it [00:00, ?it/s]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"`Trainer.fit` stopped: `max_epochs=1000` reached.\n"
]
}
],
"source": [
"# make model + solver + trainer\n",
"model = FeedForward(\n",
" layers=[10, 10],\n",
" func=Softplus,\n",
" output_dimensions=len(problem.output_variables),\n",
" input_dimensions=len(problem.input_variables)\n",
")\n",
"pinn = PINN(problem, model, optimizer_kwargs={'lr':0.006, 'weight_decay':1e-8})\n",
"trainer = Trainer(pinn, max_epochs=1000, callbacks=[MetricTracker()], accelerator='cpu', enable_model_summary=False) # we train on CPU and avoid model summary at beginning of training (optional)\n",
"\n",
"# train\n",
"trainer.train()"
]
},
{
"cell_type": "markdown",
"id": "eb83cc7a",
"metadata": {},
"source": [
"Now the `Plotter` class is used to plot the results.\n",
"The solution predicted by the neural network is plotted on the left, the exact one is represented at the center and on the right the error between the exact and the predicted solutions is showed. "
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "1ab83c03",
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 1600x600 with 6 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plotter = Plotter()\n",
"plotter.plot(trainer)"
]
},
{
"cell_type": "markdown",
"id": "20fdf23e",
"metadata": {},
"source": [
"## Solving the problem with extra-features PINNs"
]
},
{
"cell_type": "markdown",
"id": "a1e76351",
"metadata": {},
"source": [
"Now, the same problem is solved in a different way.\n",
"A new neural network is now defined, with an additional input variable, named extra-feature, which coincides with the forcing term in the Laplace equation. \n",
"The set of input variables to the neural network is:\n",
"\n",
"\\begin{equation}\n",
"[x, y, k(x, y)], \\text{ with } k(x, y)=\\sin{(\\pi x)}\\sin{(\\pi y)},\n",
"\\end{equation}\n",
"\n",
"where $x$ and $y$ are the spatial coordinates and $k(x, y)$ is the added feature. \n",
"\n",
"This feature is initialized in the class `SinSin`, which needs to be inherited by the `torch.nn.Module` class and to have the `forward` method. After declaring such feature, we can just incorporate in the `FeedForward` class thanks to the `extra_features` argument.\n",
"**NB**: `extra_features` always needs a `list` as input, you you have one feature just encapsulated it in a class, as in the next cell.\n",
"\n",
"Finally, we perform the same training as before: the problem is `Poisson`, the network is composed by the same number of neurons and optimizer parameters are equal to previous test, the only change is the new extra feature."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "ef3ad372",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"GPU available: False, used: False\n",
"TPU available: False, using: 0 TPU cores\n",
"IPU available: False, using: 0 IPUs\n",
"HPU available: False, using: 0 HPUs\n"
]
},
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "317bf4c6dbf3477e907fdc93d11140c2",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"Training: 0it [00:00, ?it/s]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"`Trainer.fit` stopped: `max_epochs=1000` reached.\n"
]
}
],
"source": [
"class SinSin(torch.nn.Module):\n",
" \"\"\"Feature: sin(x)*sin(y)\"\"\"\n",
" def __init__(self):\n",
" super().__init__()\n",
"\n",
" def forward(self, x):\n",
" t = (torch.sin(x.extract(['x'])*torch.pi) *\n",
" torch.sin(x.extract(['y'])*torch.pi))\n",
" return LabelTensor(t, ['sin(x)sin(y)'])\n",
"\n",
"\n",
"# make model + solver + trainer\n",
"model_feat = FeedForward(\n",
" layers=[10, 10],\n",
" func=Softplus,\n",
" output_dimensions=len(problem.output_variables),\n",
" input_dimensions=len(problem.input_variables)+1\n",
")\n",
"pinn_feat = PINN(problem, model_feat, extra_features=[SinSin()], optimizer_kwargs={'lr':0.006, 'weight_decay':1e-8})\n",
"trainer_feat = Trainer(pinn_feat, max_epochs=1000, callbacks=[MetricTracker()], accelerator='cpu', enable_model_summary=False) # we train on CPU and avoid model summary at beginning of training (optional)\n",
"\n",
"# train\n",
"trainer_feat.train()"
]
},
{
"cell_type": "markdown",
"id": "9748a13e",
"metadata": {},
"source": [
"The predicted and exact solutions and the error between them are represented below.\n",
"We can easily note that now our network, having almost the same condition as before, is able to reach additional order of magnitudes in accuracy."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "2be6b145",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
"<Figure size 1600x600 with 6 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plotter.plot(trainer_feat)"
]
},
{
"cell_type": "markdown",
"id": "e7bc0577",
"metadata": {},
"source": [
"## Solving the problem with learnable extra-features PINNs"
]
},
{
"cell_type": "markdown",
"id": "86c1d7b0",
"metadata": {},
"source": [
"We can still do better!\n",
"\n",
"Another way to exploit the extra features is the addition of learnable parameter inside them.\n",
"In this way, the added parameters are learned during the training phase of the neural network. In this case, we use:\n",
"\n",
"\\begin{equation}\n",
"k(x, \\mathbf{y}) = \\beta \\sin{(\\alpha x)} \\sin{(\\alpha y)},\n",
"\\end{equation}\n",
"\n",
"where $\\alpha$ and $\\beta$ are the abovementioned parameters.\n",
"Their implementation is quite trivial: by using the class `torch.nn.Parameter` we cam define all the learnable parameters we need, and they are managed by `autograd` module!"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "ae8716e7",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"GPU available: False, used: False\n",
"TPU available: False, using: 0 TPU cores\n",
"IPU available: False, using: 0 IPUs\n",
"HPU available: False, using: 0 HPUs\n"
]
},
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "6a053d5d0430499aa83a8df69ffb19f6",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"Training: 0it [00:00, ?it/s]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"`Trainer.fit` stopped: `max_epochs=1000` reached.\n"
]
}
],
"source": [
"class SinSinAB(torch.nn.Module):\n",
" \"\"\" \"\"\"\n",
" def __init__(self):\n",
" super().__init__()\n",
" self.alpha = torch.nn.Parameter(torch.tensor([1.0]))\n",
" self.beta = torch.nn.Parameter(torch.tensor([1.0]))\n",
"\n",
"\n",
" def forward(self, x):\n",
" t = (\n",
" self.beta*torch.sin(self.alpha*x.extract(['x'])*torch.pi)*\n",
" torch.sin(self.alpha*x.extract(['y'])*torch.pi)\n",
" )\n",
" return LabelTensor(t, ['b*sin(a*x)sin(a*y)'])\n",
"\n",
"\n",
"# make model + solver + trainer\n",
"model_lean= FeedForward(\n",
" layers=[10, 10],\n",
" func=Softplus,\n",
" output_dimensions=len(problem.output_variables),\n",
" input_dimensions=len(problem.input_variables)+1\n",
")\n",
"pinn_lean = PINN(problem, model_lean, extra_features=[SinSinAB()], optimizer_kwargs={'lr':0.006, 'weight_decay':1e-8})\n",
"trainer_learn = Trainer(pinn_lean, max_epochs=1000, accelerator='cpu', enable_model_summary=False) # we train on CPU and avoid model summary at beginning of training (optional)\n",
"\n",
"# train\n",
"trainer_learn.train()"
]
},
{
"cell_type": "markdown",
"id": "0319fb3b",
"metadata": {},
"source": [
"Umh, the final loss is not appreciabily better than previous model (with static extra features), despite the usage of learnable parameters. This is mainly due to the over-parametrization of the network: there are many parameter to optimize during the training, and the model in unable to understand automatically that only the parameters of the extra feature (and not the weights/bias of the FFN) should be tuned in order to fit our problem. A longer training can be helpful, but in this case the faster way to reach machine precision for solving the Poisson problem is removing all the hidden layers in the `FeedForward`, keeping only the $\\alpha$ and $\\beta$ parameters of the extra feature."
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "daa9cf17",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"GPU available: False, used: False\n",
"TPU available: False, using: 0 TPU cores\n",
"IPU available: False, using: 0 IPUs\n",
"HPU available: False, using: 0 HPUs\n"
]
},
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "a99e60c9aa61432cbae59b914ce973d2",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"Training: 0it [00:00, ?it/s]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"`Trainer.fit` stopped: `max_epochs=1000` reached.\n"
]
}
],
"source": [
"# make model + solver + trainer\n",
"model_lean= FeedForward(\n",
" layers=[],\n",
" func=Softplus,\n",
" output_dimensions=len(problem.output_variables),\n",
" input_dimensions=len(problem.input_variables)+1\n",
")\n",
"pinn_learn = PINN(problem, model_lean, extra_features=[SinSinAB()], optimizer_kwargs={'lr':0.006, 'weight_decay':1e-8})\n",
"trainer_learn = Trainer(pinn_learn, max_epochs=1000, callbacks=[MetricTracker()], accelerator='cpu', enable_model_summary=False) # we train on CPU and avoid model summary at beginning of training (optional)\n",
"\n",
"# train\n",
"trainer_learn.train()"
]
},
{
"cell_type": "markdown",
"id": "150b3e62",
"metadata": {},
"source": [
"In such a way, the model is able to reach a very high accuracy!\n",
"Of course, this is a toy problem for understanding the usage of extra features: similar precision could be obtained if the extra features are very similar to the true solution. The analyzed Poisson problem shows a forcing term very close to the solution, resulting in a perfect problem to address with such an approach.\n",
"\n",
"We conclude here by showing the graphical comparison of the unknown field and the loss trend for all the test cases presented here: the standard PINN, PINN with extra features, and PINN with learnable extra features."
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "96e51c43",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 1600x600 with 6 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plotter.plot(trainer_learn)"
]
},
{
"cell_type": "markdown",
"id": "8c64fcb4",
"metadata": {},
"source": [
"Let us compare the training losses for the various types of training"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "2855cea1",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plotter.plot_loss(trainer, label='Standard')\n",
"plotter.plot_loss(trainer_feat, label='Static Features')\n",
"plotter.plot_loss(trainer_learn, label='Learnable Features')\n"
]
},
{
"cell_type": "markdown",
"id": "0a4c8895",
"metadata": {},
"source": [
"## What's next?\n",
"\n",
"Nice you have completed the two dimensional Poisson tutorial of **PINA**! 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. Propose new types of extrafeatures and see how they affect the learning\n",
"\n",
"3. Exploit extrafeature training in more complex problems\n",
"\n",
"4. Many more..."
]
}
],
"metadata": {
"interpreter": {
"hash": "56be7540488f3dc66429ddf54a0fa9de50124d45fcfccfaf04c4c3886d735a3a"
},
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"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": "3.9.7"
}
},
"nbformat": 4,
"nbformat_minor": 5
}