{ "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": [ "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, 158.53it/s, v_num=3, gamma1_loss=5.29e-5, gamma2_loss=4.09e-5, gamma3_loss=4.73e-5, gamma4_loss=4.18e-5, D_loss=0.00134, mean_loss=0.000304] " ] }, { "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, 105.33it/s, v_num=3, gamma1_loss=5.29e-5, gamma2_loss=4.09e-5, gamma3_loss=4.73e-5, gamma4_loss=4.18e-5, D_loss=0.00134, mean_loss=0.000304]\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": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plotter = Plotter()\n", "plotter.plot(solver=pinn)" ] }, { "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" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 999: : 1it [00:00, 111.88it/s, v_num=4, gamma1_loss=2.54e-7, gamma2_loss=2.17e-7, gamma3_loss=1.94e-7, gamma4_loss=2.69e-7, D_loss=9.2e-6, mean_loss=2.03e-6] " ] }, { "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, 85.62it/s, v_num=4, gamma1_loss=2.54e-7, gamma2_loss=2.17e-7, gamma3_loss=1.94e-7, gamma4_loss=2.69e-7, D_loss=9.2e-6, mean_loss=2.03e-6] \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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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plotter.plot(solver=pinn_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": 7, "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" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 999: : 1it [00:00, 119.29it/s, v_num=5, gamma1_loss=3.26e-8, gamma2_loss=7.84e-8, gamma3_loss=1.13e-7, gamma4_loss=3.02e-8, D_loss=2.66e-6, mean_loss=5.82e-7] " ] }, { "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, 85.94it/s, v_num=5, gamma1_loss=3.26e-8, gamma2_loss=7.84e-8, gamma3_loss=1.13e-7, gamma4_loss=3.02e-8, D_loss=2.66e-6, mean_loss=5.82e-7] \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": 8, "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" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 0: : 0it [00:00, ?it/s]" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 999: : 1it [00:00, 131.20it/s, v_num=6, gamma1_loss=2.55e-16, gamma2_loss=4.76e-17, gamma3_loss=2.55e-16, gamma4_loss=4.76e-17, D_loss=1.74e-13, mean_loss=3.5e-14] " ] }, { "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, 98.81it/s, v_num=6, gamma1_loss=2.55e-16, gamma2_loss=4.76e-17, gamma3_loss=2.55e-16, gamma4_loss=4.76e-17, D_loss=1.74e-13, mean_loss=3.5e-14] \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':0.01, '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": 9, "id": "96e51c43", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plotter.plot(solver=pinn_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": 10, "id": "2855cea1", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plotter.plot_loss(trainer, logy=True, label='Standard')\n", "plotter.plot_loss(trainer_feat, logy=True,label='Static Features')\n", "plotter.plot_loss(trainer_learn, logy=True, 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": "3.9.16" } }, "nbformat": 4, "nbformat_minor": 5 }