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PINA/tutorials/tutorial2/tutorial.ipynb
2023-11-17 09:51:29 +01:00

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{
"cells": [
{
"cell_type": "markdown",
"id": "de19422d",
"metadata": {},
"source": [
"# Tutorial 2: resolution of Poisson problem and usage of extra-features"
]
},
{
"cell_type": "markdown",
"id": "492a37b4",
"metadata": {},
"source": [
"### The problem definition"
]
},
{
"cell_type": "markdown",
"id": "2c0b1777",
"metadata": {},
"source": [
"This tutorial presents how to solve with Physics-Informed Neural Networks a 2D Poisson problem with Dirichlet boundary conditions. Using extrafeatures.\n",
"\n",
"The problem is 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."
]
},
{
"cell_type": "markdown",
"id": "330528d4",
"metadata": {},
"source": [
"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": "6373ff07",
"metadata": {},
"source": [
"Now, 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. *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",
" 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": [
"### The problem solution "
]
},
{
"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. These parameters can be modified as desired."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "e7d20d6d",
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/u/n/ndemo/.local/lib/python3.9/site-packages/torch/cuda/__init__.py:546: UserWarning: Can't initialize NVML\n",
" warnings.warn(\"Can't initialize NVML\")\n",
"GPU available: True (cuda), used: True\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/n/ndemo/PINA/tutorials/tutorial2/lightning_logs\n",
"2023-10-17 10:09:18.208459: I tensorflow/core/util/port.cc:110] oneDNN custom operations are on. You may see slightly different numerical results due to floating-point round-off errors from different computation orders. To turn them off, set the environment variable `TF_ENABLE_ONEDNN_OPTS=0`.\n",
"2023-10-17 10:09:18.235849: I tensorflow/core/platform/cpu_feature_guard.cc:182] This TensorFlow binary is optimized to use available CPU instructions in performance-critical operations.\n",
"To enable the following instructions: AVX2 AVX512F AVX512_VNNI FMA, in other operations, rebuild TensorFlow with the appropriate compiler flags.\n",
"2023-10-17 10:09:20.462393: W tensorflow/compiler/tf2tensorrt/utils/py_utils.cc:38] TF-TRT Warning: Could not find TensorRT\n",
"/opt/sissa/apps/intelpython/2022.0.2/intelpython/latest/lib/python3.9/site-packages/scipy/__init__.py:138: UserWarning: A NumPy version >=1.16.5 and <1.23.0 is required for this version of SciPy (detected version 1.26.0)\n",
" warnings.warn(f\"A NumPy version >={np_minversion} and <{np_maxversion} is required for this version of \"\n",
"LOCAL_RANK: 0 - CUDA_VISIBLE_DEVICES: [0]\n",
"\n",
" | Name | Type | Params\n",
"----------------------------------------\n",
"0 | _loss | MSELoss | 0 \n",
"1 | _neural_net | Network | 151 \n",
"----------------------------------------\n",
"151 Trainable params\n",
"0 Non-trainable params\n",
"151 Total params\n",
"0.001 Total estimated model params size (MB)\n"
]
},
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "f3189e1fab9a48868024a2b9cfa9d8df",
"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()])\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": "c3ae06e7",
"metadata": {},
"source": [
"### The problem solution with extra-features"
]
},
{
"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: True (cuda), used: True\n",
"TPU available: False, using: 0 TPU cores\n",
"IPU available: False, using: 0 IPUs\n",
"HPU available: False, using: 0 HPUs\n",
"LOCAL_RANK: 0 - CUDA_VISIBLE_DEVICES: [0]\n",
"\n",
" | Name | Type | Params\n",
"----------------------------------------\n",
"0 | _loss | MSELoss | 0 \n",
"1 | _neural_net | Network | 161 \n",
"----------------------------------------\n",
"161 Trainable params\n",
"0 Non-trainable params\n",
"161 Total params\n",
"0.001 Total estimated model params size (MB)\n"
]
},
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "266cc2ef726b4b68a4f3dfaed9eb3d8f",
"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()])\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": [
"### The problem solution with learnable extra-features"
]
},
{
"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": 7,
"id": "ae8716e7",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"GPU available: True (cuda), used: True\n",
"TPU available: False, using: 0 TPU cores\n",
"IPU available: False, using: 0 IPUs\n",
"HPU available: False, using: 0 HPUs\n",
"LOCAL_RANK: 0 - CUDA_VISIBLE_DEVICES: [0]\n",
"\n",
" | Name | Type | Params\n",
"----------------------------------------\n",
"0 | _loss | MSELoss | 0 \n",
"1 | _neural_net | Network | 161 \n",
"----------------------------------------\n",
"161 Trainable params\n",
"0 Non-trainable params\n",
"161 Total params\n",
"0.001 Total estimated model params size (MB)\n"
]
},
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "3412e2b4e5374ecea0abbc9eb81e5792",
"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=[SinSin()], optimizer_kwargs={'lr':0.006, 'weight_decay':1e-8})\n",
"trainer_learn = Trainer(pinn_lean, max_epochs=1000)\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": 8,
"id": "daa9cf17",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"GPU available: True (cuda), used: True\n",
"TPU available: False, using: 0 TPU cores\n",
"IPU available: False, using: 0 IPUs\n",
"HPU available: False, using: 0 HPUs\n",
"LOCAL_RANK: 0 - CUDA_VISIBLE_DEVICES: [0]\n",
"\n",
" | Name | Type | Params\n",
"----------------------------------------\n",
"0 | _loss | MSELoss | 0 \n",
"1 | _neural_net | Network | 4 \n",
"----------------------------------------\n",
"4 Trainable params\n",
"0 Non-trainable params\n",
"4 Total params\n",
"0.000 Total estimated model params size (MB)\n"
]
},
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "e16800d1d55449cc8c6be55c02e0a251",
"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=[SinSin()], optimizer_kwargs={'lr':0.006, 'weight_decay':1e-8})\n",
"trainer_learn = Trainer(pinn_learn, max_epochs=1000, callbacks=[MetricTracker()])\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": 9,
"id": "96e51c43",
"metadata": {},
"outputs": [
{
"data": {
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"text/plain": [
"<Figure size 1600x600 with 6 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plotter.plot(trainer_learn)"
]
}
],
"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
}