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PINA/tutorials/tutorial3/tutorial.ipynb
2023-11-17 09:51:29 +01:00

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{
"cells": [
{
"cell_type": "markdown",
"id": "6a739a84",
"metadata": {},
"source": [
"# Tutorial: Two dimensional Wave problem with hard constraint\n",
"\n",
"In this tutorial we present how to solve the wave equation using hard constraint PINNs. For doing so we will build a costum `torch` model and pass it to the `PINN` solver.\n",
"\n",
"First of all, some useful imports."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "d93daba0",
"metadata": {},
"outputs": [],
"source": [
"import torch\n",
"\n",
"from pina.problem import SpatialProblem, TimeDependentProblem\n",
"from pina.operators import laplacian, grad\n",
"from pina.geometry import CartesianDomain\n",
"from pina.solvers import PINN\n",
"from pina.trainer import Trainer\n",
"from pina.equation import Equation\n",
"from pina.equation.equation_factory import FixedValue\n",
"from pina import Condition, Plotter"
]
},
{
"cell_type": "markdown",
"id": "2316f24e",
"metadata": {},
"source": [
"## The problem definition "
]
},
{
"cell_type": "markdown",
"id": "bc2bbf62",
"metadata": {},
"source": [
"The problem is written in the following form:\n",
"\n",
"\\begin{equation}\n",
"\\begin{cases}\n",
"\\Delta u(x,y,t) = \\frac{\\partial^2}{\\partial t^2} u(x,y,t) \\quad \\text{in } D, \\\\\\\\\n",
"u(x, y, t=0) = \\sin(\\pi x)\\sin(\\pi y), \\\\\\\\\n",
"u(x, y, t) = 0 \\quad \\text{on } \\Gamma_1 \\cup \\Gamma_2 \\cup \\Gamma_3 \\cup \\Gamma_4,\n",
"\\end{cases}\n",
"\\end{equation}\n",
"\n",
"where $D$ is a square domain $[0,1]^2$, and $\\Gamma_i$, with $i=1,...,4$, are the boundaries of the square, and the velocity in the standard wave equation is fixed to one."
]
},
{
"cell_type": "markdown",
"id": "cbc50741",
"metadata": {},
"source": [
"Now, the wave problem is written in PINA code as a class, inheriting from `SpatialProblem` and `TimeDependentProblem` since we deal with spatial, and time dependent variables. The equations are written as `conditions` that should be satisfied in the corresponding domains. `truth_solution` is the exact solution which will be compared with the predicted one."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "b60176c4",
"metadata": {},
"outputs": [],
"source": [
"class Wave(TimeDependentProblem, SpatialProblem):\n",
" output_variables = ['u']\n",
" spatial_domain = CartesianDomain({'x': [0, 1], 'y': [0, 1]})\n",
" temporal_domain = CartesianDomain({'t': [0, 1]})\n",
"\n",
" def wave_equation(input_, output_):\n",
" u_t = grad(output_, input_, components=['u'], d=['t'])\n",
" u_tt = grad(u_t, input_, components=['dudt'], d=['t'])\n",
" nabla_u = laplacian(output_, input_, components=['u'], d=['x', 'y'])\n",
" return nabla_u - u_tt\n",
"\n",
" def initial_condition(input_, output_):\n",
" u_expected = (torch.sin(torch.pi*input_.extract(['x'])) *\n",
" torch.sin(torch.pi*input_.extract(['y'])))\n",
" return output_.extract(['u']) - u_expected\n",
"\n",
" conditions = {\n",
" 'gamma1': Condition(location=CartesianDomain({'x': [0, 1], 'y': 1, 't': [0, 1]}), equation=FixedValue(0.)),\n",
" 'gamma2': Condition(location=CartesianDomain({'x': [0, 1], 'y': 0, 't': [0, 1]}), equation=FixedValue(0.)),\n",
" 'gamma3': Condition(location=CartesianDomain({'x': 1, 'y': [0, 1], 't': [0, 1]}), equation=FixedValue(0.)),\n",
" 'gamma4': Condition(location=CartesianDomain({'x': 0, 'y': [0, 1], 't': [0, 1]}), equation=FixedValue(0.)),\n",
" 't0': Condition(location=CartesianDomain({'x': [0, 1], 'y': [0, 1], 't': 0}), equation=Equation(initial_condition)),\n",
" 'D': Condition(location=CartesianDomain({'x': [0, 1], 'y': [0, 1], 't': [0, 1]}), equation=Equation(wave_equation)),\n",
" }\n",
"\n",
" def wave_sol(self, pts):\n",
" return (torch.sin(torch.pi*pts.extract(['x'])) *\n",
" torch.sin(torch.pi*pts.extract(['y'])) *\n",
" torch.cos(torch.sqrt(torch.tensor(2.))*torch.pi*pts.extract(['t'])))\n",
"\n",
" truth_solution = wave_sol\n",
"\n",
"problem = Wave()"
]
},
{
"cell_type": "markdown",
"id": "03557e0c-1f82-4dad-b611-5d33fddfd0ef",
"metadata": {},
"source": [
"## Hard Constraint Model"
]
},
{
"cell_type": "markdown",
"id": "356fe363",
"metadata": {},
"source": [
"After the problem, a **torch** model is needed to solve the PINN. Usually, many models are already implemented in **PINA**, but the user has the possibility to build his/her own model in `torch`. The hard constraint we impose is on the boundary of the spatial domain. Specifically, our solution is written as:\n",
"\n",
"$$ u_{\\rm{pinn}} = xy(1-x)(1-y)\\cdot NN(x, y, t), $$\n",
"\n",
"where $NN$ is the neural net output. This neural network takes as input the coordinates (in this case $x$, $y$ and $t$) and provides the unknown field $u$. By construction, it is zero on the boundaries. The residuals of the equations are evaluated at several sampling points (which the user can manipulate using the method `discretise_domain`) and the loss minimized by the neural network is the sum of the residuals."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "9fbbb74f",
"metadata": {},
"outputs": [],
"source": [
"class HardMLP(torch.nn.Module):\n",
"\n",
" def __init__(self, input_dim, output_dim):\n",
" super().__init__()\n",
"\n",
" self.layers = torch.nn.Sequential(torch.nn.Linear(input_dim, 40),\n",
" torch.nn.ReLU(),\n",
" torch.nn.Linear(40, 40),\n",
" torch.nn.ReLU(),\n",
" torch.nn.Linear(40, output_dim))\n",
" \n",
" # here in the foward we implement the hard constraints\n",
" def forward(self, x):\n",
" hard = x.extract(['x'])*(1-x.extract(['x']))*x.extract(['y'])*(1-x.extract(['y']))\n",
" return hard*self.layers(x)"
]
},
{
"cell_type": "markdown",
"id": "f79fc901-4720-4fac-8b72-84ac5f7d2ec3",
"metadata": {},
"source": [
"## Train and Inference"
]
},
{
"cell_type": "markdown",
"id": "b465bebd",
"metadata": {},
"source": [
"In this tutorial, the neural network is trained for 1000 epochs with a learning rate of 0.001 (default in `PINN`). Training takes approximately 3 minutes."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "0be8e7f5",
"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",
"Missing logger folder: /Users/dariocoscia/Desktop/PINA/tutorials/tutorial3/lightning_logs\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Epoch 999: : 1it [00:00, 62.13it/s, v_num=0, mean_loss=0.0268, D_loss=0.0397, t0_loss=0.121, gamma1_loss=0.000, gamma2_loss=0.000, gamma3_loss=0.000, gamma4_loss=0.000] "
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"`Trainer.fit` stopped: `max_epochs=1000` reached.\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Epoch 999: : 1it [00:00, 53.88it/s, v_num=0, mean_loss=0.0268, D_loss=0.0397, t0_loss=0.121, gamma1_loss=0.000, gamma2_loss=0.000, gamma3_loss=0.000, gamma4_loss=0.000]\n"
]
}
],
"source": [
"# generate the data\n",
"problem.discretise_domain(1000, 'random', locations=['D', 't0', 'gamma1', 'gamma2', 'gamma3', 'gamma4'])\n",
"\n",
"# crete the solver\n",
"pinn = PINN(problem, HardMLP(len(problem.input_variables), len(problem.output_variables)))\n",
"\n",
"# create trainer and train\n",
"trainer = Trainer(pinn, max_epochs=1000, accelerator='cpu', enable_model_summary=False) # we train on CPU and avoid model summary at beginning of training (optional)\n",
"trainer.train()"
]
},
{
"cell_type": "markdown",
"id": "c2a5c405",
"metadata": {},
"source": [
"Notice that the loss on the boundaries of the spatial domain is exactly zero, as expected! After the training is completed one can now plot some results using the `Plotter` class of **PINA**."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "c086c05f",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Plotting at t=0\n"
]
},
{
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"text/plain": [
"<Figure size 1600x600 with 6 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Plotting at t=0.5\n"
]
},
{
"data": {
"image/png": 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"text/plain": [
"<Figure size 1600x600 with 6 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Plotting at t=1\n"
]
},
{
"data": {
"image/png": 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"text/plain": [
"<Figure size 1600x600 with 6 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plotter = Plotter()\n",
"\n",
"# plotting at fixed time t = 0.0\n",
"print('Plotting at t=0')\n",
"plotter.plot(pinn, fixed_variables={'t': 0.0})\n",
"\n",
"# plotting at fixed time t = 0.5\n",
"print('Plotting at t=0.5')\n",
"plotter.plot(pinn, fixed_variables={'t': 0.5})\n",
"\n",
"# plotting at fixed time t = 1.\n",
"print('Plotting at t=1')\n",
"plotter.plot(pinn, fixed_variables={'t': 1.0})"
]
},
{
"cell_type": "markdown",
"id": "35e51649",
"metadata": {},
"source": [
"The results are not so great, and we can clearly see that as time progress the solution get worse.... Can we do better?\n",
"\n",
"A valid option is to impose the initial condition as hard constraint as well. Specifically, our solution is written as:\n",
"\n",
"$$ u_{\\rm{pinn}} = xy(1-x)(1-y)\\cdot NN(x, y, t)\\cdot t + \\cos(\\sqrt{2}\\pi t)sin(\\pi x)\\sin(\\pi y), $$\n",
"\n",
"Let us build the network first"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "33e43412",
"metadata": {},
"outputs": [],
"source": [
"class HardMLPtime(torch.nn.Module):\n",
"\n",
" def __init__(self, input_dim, output_dim):\n",
" super().__init__()\n",
"\n",
" self.layers = torch.nn.Sequential(torch.nn.Linear(input_dim, 40),\n",
" torch.nn.ReLU(),\n",
" torch.nn.Linear(40, 40),\n",
" torch.nn.ReLU(),\n",
" torch.nn.Linear(40, output_dim))\n",
" \n",
" # here in the foward we implement the hard constraints\n",
" def forward(self, x):\n",
" hard_space = x.extract(['x'])*(1-x.extract(['x']))*x.extract(['y'])*(1-x.extract(['y']))\n",
" hard_t = torch.sin(torch.pi*x.extract(['x'])) * torch.sin(torch.pi*x.extract(['y'])) * torch.cos(torch.sqrt(torch.tensor(2.))*torch.pi*x.extract(['t']))\n",
" return hard_space * self.layers(x) * x.extract(['t']) + hard_t"
]
},
{
"cell_type": "markdown",
"id": "5d3dc67b",
"metadata": {},
"source": [
"Now let's train with the same configuration as thre previous test"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "f4bc6be2",
"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"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Epoch 999: : 1it [00:00, 48.54it/s, v_num=1, mean_loss=1.48e-8, D_loss=8.89e-8, t0_loss=0.000, gamma1_loss=2.06e-15, gamma2_loss=0.000, gamma3_loss=2.1e-15, gamma4_loss=0.000]"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"`Trainer.fit` stopped: `max_epochs=1000` reached.\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Epoch 999: : 1it [00:00, 43.25it/s, v_num=1, mean_loss=1.48e-8, D_loss=8.89e-8, t0_loss=0.000, gamma1_loss=2.06e-15, gamma2_loss=0.000, gamma3_loss=2.1e-15, gamma4_loss=0.000]\n"
]
}
],
"source": [
"# generate the data\n",
"problem.discretise_domain(1000, 'random', locations=['D', 't0', 'gamma1', 'gamma2', 'gamma3', 'gamma4'])\n",
"\n",
"# crete the solver\n",
"pinn = PINN(problem, HardMLPtime(len(problem.input_variables), len(problem.output_variables)))\n",
"\n",
"# create trainer and train\n",
"trainer = Trainer(pinn, max_epochs=1000, accelerator='cpu', enable_model_summary=False) # we train on CPU and avoid model summary at beginning of training (optional)\n",
"trainer.train()"
]
},
{
"cell_type": "markdown",
"id": "a0f80cb8",
"metadata": {},
"source": [
"We can clearly see that the loss is way lower now. Let's plot the results"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "019767e5",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Plotting at t=0\n"
]
},
{
"data": {
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"text/plain": [
"<Figure size 1600x600 with 6 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Plotting at t=0.5\n"
]
},
{
"data": {
"image/png": 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"text/plain": [
"<Figure size 1600x600 with 6 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Plotting at t=1\n"
]
},
{
"data": {
"image/png": 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"text/plain": [
"<Figure size 1600x600 with 6 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plotter = Plotter()\n",
"\n",
"# plotting at fixed time t = 0.0\n",
"print('Plotting at t=0')\n",
"plotter.plot(pinn, fixed_variables={'t': 0.0})\n",
"\n",
"# plotting at fixed time t = 0.5\n",
"print('Plotting at t=0.5')\n",
"plotter.plot(pinn, fixed_variables={'t': 0.5})\n",
"\n",
"# plotting at fixed time t = 1.\n",
"print('Plotting at t=1')\n",
"plotter.plot(pinn, fixed_variables={'t': 1.0})"
]
},
{
"cell_type": "markdown",
"id": "b7338109",
"metadata": {},
"source": [
"We can see now that the results are way better! This is due to the fact that previously the network was not learning correctly the initial conditon, leading to a poor solution when the time evolved. By imposing the initial condition the network is able to correctly solve the problem."
]
},
{
"cell_type": "markdown",
"id": "61195b1f",
"metadata": {},
"source": [
"## What's next?\n",
"\n",
"Nice you have completed the two dimensional Wave 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 hard constraints in time, e.g. $$ u_{\\rm{pinn}} = xy(1-x)(1-y)\\cdot NN(x, y, t)(1-\\exp(-t)) + \\cos(\\sqrt{2}\\pi t)sin(\\pi x)\\sin(\\pi y), $$\n",
"\n",
"3. Exploit extrafeature training for model 1 and 2\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": "3.9.16"
}
},
"nbformat": 4,
"nbformat_minor": 5
}