{ "cells": [ { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "# Tutorial: Advection Equation with data driven DeepONet\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/tutorial24/tutorial.ipynb)\n", "\n", "\n", "> ##### ⚠️ ***Before starting:***\n", "> We assume you are already familiar with the concepts covered in the [Getting started with PINA](https://mathlab.github.io/PINA/_tutorial.html#getting-started-with-pina) tutorials. If not, we strongly recommend reviewing them before exploring this advanced topic.\n", "\n", "In this tutorial, we demonstrate how to solve the advection operator learning problem using `DeepONet`. We follow the original formulation of Lu *et al.* in [*DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operator*](https://arxiv.org/abs/1910.03193).\n", "\n", "We begin by importing the necessary modules." ] }, { "cell_type": "code", "execution_count": 1, "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", " # get the data\n", " !mkdir \"data\"\n", " !wget \"https://github.com/mathLab/PINA/raw/refs/heads/master/tutorials/tutorial24/data/advection_input_testing.pt\" -O \"data/advection_input_testing.pt\"\n", " !wget \"https://github.com/mathLab/PINA/raw/refs/heads/master/tutorials/tutorial24/data/advection_input_training.pt\" -O \"data/advection_input_training.pt\"\n", " !wget \"https://github.com/mathLab/PINA/raw/refs/heads/master/tutorials/tutorial24/data/advection_output_testing.pt\" -O \"data/advection_output_testing.pt\"\n", " !wget \"https://github.com/mathLab/PINA/raw/refs/heads/master/tutorials/tutorial24/data/advection_output_training.pt\" -O \"data/advection_output_training.pt\"\n", "\n", "import matplotlib.pyplot as plt\n", "import torch\n", "import warnings\n", "\n", "\n", "from pina import Trainer, LabelTensor\n", "from pina.model import FeedForward, DeepONet\n", "from pina.solver import SupervisedSolver\n", "from pina.problem.zoo import SupervisedProblem\n", "from pina.loss import LpLoss\n", "\n", "warnings.filterwarnings(\"ignore\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Advection problem and data preparation\n", "\n", "We consider the 1D advection equation\n", "$$\n", "\\frac{\\partial u}{\\partial t} + \\frac{\\partial u}{\\partial x} = 0, \n", "\\quad x \\in [0,2], \\; t \\in [0,1],\n", "$$\n", "with periodic boundary conditions. The initial condition is chosen as a Gaussian pulse centered at a random location\n", "$\\mu \\sim U(0.05, 1)$ and with variance $\\sigma^2 = 0.02$:\n", "$$\n", "u_0(x) = \\frac{1}{\\sqrt{\\pi\\sigma^2}} e^{-\\frac{(x - \\mu)^2}{2\\sigma^2}}, \n", "\\quad x \\in [0,2].\n", "$$\n", "\n", "Our goal is to learn the operator\n", "$$\n", "\\mathcal{G}: u_0(x) \\mapsto u(x, t = \\delta) = u_0(x - \\delta),\n", "$$\n", "with $\\delta = 0.5$ for this tutorial. In practice, this means learning a mapping from the initial condition to the solution at a fixed later time. \n", "The dataset therefore consists of trajectories where inputs are initial profiles and outputs are the same profiles shifted by $\\delta$.\n", "\n", "The data has shape `[T, Nx, D]`, where:\n", "- `T` — number of trajectories (100 for training, 1000 for testing),\n", "- `Nx` — number of spatial grid points (fixed at 100),\n", "- `D = 1` — single scalar field value `u`.\n", "\n", "We now load the dataset and visualize sample trajectories." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# loading training data\n", "data_0_training = LabelTensor(\n", " torch.load(\"data/advection_input_training.pt\", weights_only=False),\n", " labels=\"u0\",\n", ")\n", "data_dt_training = LabelTensor(\n", " torch.load(\"data/advection_output_training.pt\", weights_only=False),\n", " labels=\"u\",\n", ")\n", "\n", "# loading testing data\n", "data_0_testing = LabelTensor(\n", " torch.load(\"data/advection_input_testing.pt\", weights_only=False),\n", " labels=\"u0\",\n", ")\n", "data_dt_testing = LabelTensor(\n", " torch.load(\"data/advection_output_testing.pt\", weights_only=False),\n", " labels=\"u\",\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The data are loaded, let's visualize a few of the initial conditions!" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# storing the discretization in space:\n", "Nx = data_0_training.shape[1]\n", "\n", "for idx, i in enumerate(torch.randint(0, data_0_training.shape[0] - 1, (3,))):\n", " u0 = data_0_training[int(i)].extract(\"u0\")\n", " u = data_dt_training[int(i)].extract(\"u\")\n", " x = torch.linspace(\n", " 0, 2, Nx\n", " ) # the discretization in the spatial dimension is fixed\n", " plt.subplot(3, 1, idx + 1)\n", " plt.plot(x, u0.flatten(), label=rf\"$u_0(x)$\")\n", " plt.plot(x, u.flatten(), label=rf\"$u(x, t=\\delta)$\")\n", " plt.xlabel(rf\"$x$\")\n", " plt.tight_layout()\n", " plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Great — we have generated a traveling wave and visualized a few samples. Next, we will use this data to train a `DeepONet`.\n", "\n", "## DeepONet\n", "\n", "The standard `DeepONet` architecture consists of two subnetworks: a **branch** network and a **trunk** network (see figure below).\n", "\n", "
\n", "\"image\n", "
\n", "
\n", "Image source: Moya & Lin (2022)\n", "
\n", "\n", "In our setting:\n", "- The **branch network** receives the initial condition of each trajectory, with input shape `[B, Nx]` — where `B` is the batch size and `Nx` the spatial discretization points of the field at \\( t = 0 \\).\n", "- The **trunk network** takes input of shape `[B, 1]`, corresponding to the location at which we evaluate the solution (in this 1D case, the spatial coordinate).\n", "\n", "Together, these networks learn the mapping from the initial field to the solution at a later time.\n", "\n", "We now define and train the model for the advection problem." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "problem = SupervisedProblem(\n", " input_=data_0_training,\n", " output_=data_dt_training,\n", " input_variables=data_0_training.labels,\n", " output_variables=data_dt_training.labels,\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now proceede to create the trunk and branch networks." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# create Trunk model\n", "class TrunkNet(torch.nn.Module):\n", " def __init__(self, **kwargs):\n", " super().__init__()\n", " self.trunk = FeedForward(**kwargs)\n", "\n", " def forward(self, x):\n", " t = (\n", " torch.zeros(size=(x.shape[0], 1), requires_grad=False) + 0.5\n", " ) # create an input of only 0.5\n", " return self.trunk(t)\n", "\n", "\n", "# create Branch model\n", "class BranchNet(torch.nn.Module):\n", " def __init__(self, **kwargs):\n", " super().__init__()\n", " self.branch = FeedForward(**kwargs)\n", "\n", " def forward(self, x):\n", " return self.branch(x.flatten(1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `TrunkNet` is implemented as a standard `FeedForward` network with a slightly modified `forward` method. In this case, the trunk network simply outputs a tensor filled with the value \\(0.5\\), repeated for each trajectory — corresponding to evaluating the solution at time \\(t = 0.5\\).\n", "\n", "The `BranchNet` is also a `FeedForward` network, but its `forward` pass first flattens the input along the last dimension. This produces a vector of length `Nx`, representing the sampled initial condition at the sensor locations.\n", "\n", "With both subnetworks defined, we can now instantiate the DeepONet model using the `DeepONet` class from `pina.model`." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# initialize truck and branch net\n", "trunk = TrunkNet(\n", " layers=[256] * 4,\n", " output_dimensions=Nx,\n", " input_dimensions=1, # time variable dimension\n", " func=torch.nn.ReLU,\n", ")\n", "branch = BranchNet(\n", " layers=[256] * 4,\n", " output_dimensions=Nx,\n", " input_dimensions=Nx, # spatial variable dimension\n", " func=torch.nn.ReLU,\n", ")\n", "\n", "# initialize the DeepONet model\n", "model = DeepONet(\n", " branch_net=branch,\n", " trunk_net=trunk,\n", " input_indeces_branch_net=[\"u0\"],\n", " input_indeces_trunk_net=[\"u0\"],\n", " reduction=\"id\",\n", " aggregator=\"*\",\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The aggregation and reduction functions combine the outputs of the branch and trunk networks. In this example, their outputs are multiplied element-wise, and no reduction is applied — meaning the final output has the same dimensionality as each network’s output.\n", "\n", "We train the model using a `SupervisedSolver` with an `MSE` loss. Below, we first define the solver and then the trainer used to run the optimization." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# define solver\n", "solver = SupervisedSolver(problem=problem, model=model)\n", "\n", "# define the trainer and train\n", "trainer = Trainer(\n", " solver=solver, max_epochs=200, enable_model_summary=False, accelerator=\"cpu\"\n", ")\n", "trainer.train()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's see the final train and test errors:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Training error: 0.73%\n", "Testing error: 1.43%\n" ] } ], "source": [ "# the l2 error\n", "l2 = LpLoss()\n", "\n", "with torch.no_grad():\n", " train_err = l2(trainer.solver(data_0_training), data_dt_training)\n", " test_err = l2(trainer.solver(data_0_testing), data_dt_testing)\n", "\n", "print(f\"Training error: {float(train_err.mean()):.2%}\")\n", "print(f\"Testing error: {float(test_err.mean()):.2%}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that the testing error is slightly higher than the training one, maybe due to overfitting. We now plot some results trajectories." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for i in [1, 2, 3]:\n", " plt.subplot(3, 1, i)\n", " plt.plot(\n", " torch.linspace(0, 2, Nx),\n", " solver(data_0_training)[10 * i].detach().flatten(),\n", " label=r\"$u_{NN}$\",\n", " )\n", " plt.plot(\n", " torch.linspace(0, 2, Nx),\n", " data_dt_training[10 * i].extract(\"u\").flatten(),\n", " label=r\"$u$\",\n", " )\n", " plt.xlabel(r\"$x$\")\n", " plt.legend(loc=\"upper right\")\n", " plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we can see, they are barely indistinguishable. To better understand the difference, we now plot the residuals, i.e. the difference of the exact solution and the predicted one. " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for i in [1, 2, 3]:\n", " plt.subplot(3, 1, i)\n", " plt.plot(\n", " torch.linspace(0, 2, Nx),\n", " data_dt_training[10 * i].extract(\"u\").flatten()\n", " - solver(data_0_training)[10 * i].detach().flatten(),\n", " label=r\"$u - u_{NN}$\",\n", " )\n", " plt.xlabel(r\"$x$\")\n", " plt.tight_layout()\n", " plt.legend(loc=\"upper right\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## What's Next?\n", "\n", "We have seen a simple example of using `DeepONet` to learn the advection operator. This only scratches the surface of what neural operators can do. Here are some suggested directions to continue your exploration:\n", "\n", "1. **Train on more complex PDEs**: Extend beyond the advection equation to more challenging operators, such as diffusion or nonlinear conservation laws.\n", "\n", "2. **Increase training scope**: Experiment with larger datasets, deeper networks, and longer training schedules to unlock the full potential of neural operator learning.\n", "\n", "3. **Generalize to the full advection operator**: Train the model to learn the general operator $\\mathcal{G}_t: u_0(x) \\mapsto u(x,t) = u_0(x - t)$ so the network predicts solutions for arbitrary times, not just a single fixed horizon.\n", "\n", "4. **Investigate architectural variations**: Compare different operator learning architectures (e.g., Fourier Neural Operators, Physics-Informed DeepONets) to see how they perform on similar problems.\n", "\n", "5. **...and much more!**: From adding noise robustness to testing on real scientific datasets, the space of possibilities is wide open.\n", "\n", "For more resources and tutorials, check out the [PINA Documentation](https://mathlab.github.io/PINA/)." ] } ], "metadata": { "kernelspec": { "display_name": "deep", "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": "3.12.11" } }, "nbformat": 4, "nbformat_minor": 4 }