From cdbb140a4ed4126826db02008a9f9c38ca877a1e Mon Sep 17 00:00:00 2001 From: Dario Coscia Date: Sat, 1 Nov 2025 13:36:45 +0100 Subject: [PATCH] deeponet tutorial --- docs/source/_tutorial.rst | 3 +- pina/model/deeponet.py | 26 +- tests/test_model/test_deeponet.py | 16 +- tests/test_model/test_mionet.py | 9 - tutorials/README.md | 3 +- tutorials/static/deeponet.png | Bin 0 -> 359826 bytes .../data/advection_input_testing.pt | Bin 0 -> 401753 bytes .../data/advection_input_training.pt | Bin 0 -> 41760 bytes .../data/advection_output_testing.pt | Bin 0 -> 401760 bytes .../data/advection_output_training.pt | Bin 0 -> 41767 bytes tutorials/tutorial24/tutorial.ipynb | 490 ++++++++++++++++++ 11 files changed, 502 insertions(+), 45 deletions(-) create mode 100644 tutorials/static/deeponet.png create mode 100644 tutorials/tutorial24/data/advection_input_testing.pt create mode 100644 tutorials/tutorial24/data/advection_input_training.pt create mode 100644 tutorials/tutorial24/data/advection_output_testing.pt create mode 100644 tutorials/tutorial24/data/advection_output_training.pt create mode 100644 tutorials/tutorial24/tutorial.ipynb diff --git a/docs/source/_tutorial.rst b/docs/source/_tutorial.rst index 0bcc62418..99958ffcd 100644 --- a/docs/source/_tutorial.rst +++ b/docs/source/_tutorial.rst @@ -33,6 +33,7 @@ Neural Operator Learning - `Introductory Tutorial: Neural Operator Learning with PINA `_ - `Modeling 2D Darcy Flow with the Fourier Neural Operator `_ - `Solving the Kuramoto-Sivashinsky Equation with Averaging Neural Operator `_ +- `Advection Equation with data driven DeepONet `_ Supervised Learning ------------------- @@ -42,4 +43,4 @@ Supervised Learning - `Reduced Order Model with Graph Neural Networks for Unstructured Domains `_ - `Data-driven System Identification with SINDy `_ - `Unstructured Convolutional Autoencoders with Continuous Convolution `_ -- `Reduced Order Modeling with POD-RBF and POD-NN Approaches for Fluid Dynamics `_ +- `Reduced Order Modeling with POD-RBF and POD-NN Approaches for Fluid Dynamics `_ \ No newline at end of file diff --git a/pina/model/deeponet.py b/pina/model/deeponet.py index 6da161665..c65f6b316 100644 --- a/pina/model/deeponet.py +++ b/pina/model/deeponet.py @@ -52,7 +52,8 @@ def __init__( :param reduction: The reduction to be used to reduce the aggregated result of the modules in ``networks`` to the desired output dimension. Available reductions include: sum: ``+``, product: ``*``, - mean: ``mean``, min: ``min``, max: ``max``. Default is ``+``. + mean: ``mean``, min: ``min``, max: ``max``, identity: "id". + Default is ``+``. :type reduction: str or Callable :param bool scale: If ``True``, the final output is scaled before being returned in the forward pass. Default is ``True``. @@ -122,18 +123,8 @@ def __init__( check_consistency(scale, bool) check_consistency(translation, bool) - # check trunk branch nets consistency - shapes = [] - for key, value in networks.items(): + for value in networks.values(): check_consistency(value, (str, int)) - check_consistency(key, torch.nn.Module) - input_ = torch.rand(10, len(value)) - shapes.append(key(input_).shape[-1]) - - if not all(map(lambda x: x == shapes[0], shapes)): - raise ValueError( - "The passed networks have not the same output dimension." - ) # assign trunk and branch net with their input indeces self.models = torch.nn.ModuleList(networks.keys()) @@ -171,6 +162,7 @@ def _symbol_functions(**kwargs): "mean": partial(torch.mean, **kwargs), "min": lambda x: torch.min(x, **kwargs).values, "max": lambda x: torch.max(x, **kwargs).values, + "id": lambda x: x, } def _init_aggregator(self, aggregator): @@ -181,7 +173,7 @@ def _init_aggregator(self, aggregator): :type aggregator: str or Callable :raises ValueError: If the aggregator is not supported. """ - aggregator_funcs = self._symbol_functions(dim=2) + aggregator_funcs = self._symbol_functions(dim=-1) if aggregator in aggregator_funcs: aggregator_func = aggregator_funcs[aggregator] elif isinstance(aggregator, nn.Module) or is_function(aggregator): @@ -264,13 +256,9 @@ def forward(self, x): # reduce output_ = self._reduction(aggregated) if self._reduction_type in self._symbol_functions(dim=-1): - output_ = output_.reshape(-1, 1) - - # scale and translate - output_ *= self._scale - output_ += self._trasl + output_ = output_.reshape(*output_.shape, 1) - return output_ + return self._scale * output_ + self._trasl @property def aggregator(self): diff --git a/tests/test_model/test_deeponet.py b/tests/test_model/test_deeponet.py index 8917811c5..4daa55af4 100644 --- a/tests/test_model/test_deeponet.py +++ b/tests/test_model/test_deeponet.py @@ -9,7 +9,7 @@ data = torch.rand((20, 3)) input_vars = ["a", "b", "c"] input_ = LabelTensor(data, input_vars) -symbol_funcs_red = DeepONet._symbol_functions(dim=-1) +symbol_funcs_red = DeepONet._symbol_functions() output_dims = [1, 5, 10, 20] @@ -26,20 +26,6 @@ def test_constructor(): ) -def test_constructor_fails_when_invalid_inner_layer_size(): - branch_net = FeedForward(input_dimensions=1, output_dimensions=10) - trunk_net = FeedForward(input_dimensions=2, output_dimensions=8) - with pytest.raises(ValueError): - DeepONet( - branch_net=branch_net, - trunk_net=trunk_net, - input_indeces_branch_net=["a"], - input_indeces_trunk_net=["b", "c"], - reduction="+", - aggregator="*", - ) - - def test_forward_extract_str(): branch_net = FeedForward(input_dimensions=1, output_dimensions=10) trunk_net = FeedForward(input_dimensions=2, output_dimensions=10) diff --git a/tests/test_model/test_mionet.py b/tests/test_model/test_mionet.py index 4d59433bf..6e6f57934 100644 --- a/tests/test_model/test_mionet.py +++ b/tests/test_model/test_mionet.py @@ -18,15 +18,6 @@ def test_constructor(): MIONet(networks=networks, reduction="+", aggregator="*") -def test_constructor_fails_when_invalid_inner_layer_size(): - branch_net1 = FeedForward(input_dimensions=1, output_dimensions=10) - branch_net2 = FeedForward(input_dimensions=2, output_dimensions=10) - trunk_net = FeedForward(input_dimensions=1, output_dimensions=12) - networks = {branch_net1: ["x"], branch_net2: ["x", "y"], trunk_net: ["z"]} - with pytest.raises(ValueError): - MIONet(networks=networks, reduction="+", aggregator="*") - - def test_forward_extract_str(): branch_net1 = FeedForward(input_dimensions=1, output_dimensions=10) branch_net2 = FeedForward(input_dimensions=1, output_dimensions=10) diff --git a/tutorials/README.md b/tutorials/README.md index 62150ee67..949f7d6e2 100644 --- a/tutorials/README.md +++ b/tutorials/README.md @@ -36,6 +36,8 @@ Learning Bifurcating PDE Solutions with Physics-Informed Deep Ensembles|[[.ipynb Introductory Tutorial: Neural Operator Learning with PINA |[[.ipynb](tutorial21/tutorial.ipynb),[.py](tutorial21/tutorial.py),[.html](http://mathlab.github.io/PINA/tutorial21/tutorial.html)]| Modeling 2D Darcy Flow with the Fourier Neural Operator |[[.ipynb](tutorial5/tutorial.ipynb),[.py](tutorial5/tutorial.py),[.html](http://mathlab.github.io/PINA/tutorial5/tutorial.html)]| Solving the Kuramoto–Sivashinsky Equation with Averaging Neural Operator |[[.ipynb](tutorial10/tutorial.ipynb),[.py](tutorial10/tutorial.py),[.html](http://mathlab.github.io/PINA/tutorial10/tutorial.html)]| +Advection Equation with data driven DeepONet| [[.ipynb](tutorial24/tutorial.ipynb),[.py](tutorial24/tutorial.py),[.html](http://mathlab.github.io/PINA/tutorial24/tutorial.html)]| + ## Supervised Learning | Description | Tutorial | @@ -46,4 +48,3 @@ Reduced Order Model with Graph Neural Networks for Unstructured Domains| [[.ipyn Data-driven System Identification with SINDy| [[.ipynb](tutorial23/tutorial.ipynb),[.py](tutorial23/tutorial.py),[.html](http://mathlab.github.io/PINA/tutorial23/tutorial.html)]| Unstructured Convolutional Autoencoders with Continuous Convolution |[[.ipynb](tutorial4/tutorial.ipynb),[.py](tutorial4/tutorial.py),[.html](http://mathlab.github.io/PINA/tutorial4/tutorial.html)]| Reduced Order Modeling with POD-RBF and POD-NN Approaches for Fluid Dynamics| [[.ipynb](tutorial8/tutorial.ipynb),[.py](tutorial8/tutorial.py),[.html](http://mathlab.github.io/PINA/tutorial8/tutorial.html)]| - diff --git a/tutorials/static/deeponet.png b/tutorials/static/deeponet.png new file mode 100644 index 0000000000000000000000000000000000000000..acab017de2cc28780744528f119135c3c175f090 GIT binary patch literal 359826 zcmeFZc|6o@`#)^WQkIa)GPX(xC6sj(vXdxfO$f=p8)JzqDZ6AZyDWq3j3JfmRE&Me znq}-W7|V0c)pf^x-QVByz5jh)&(G_{eEQ61IhW%+j`#6C-e;k=HI-3gWdGRusRa>{a%h|$#eJO?=2U~| z$jELIN@Xe}6}OmQEWJL_FGc#eNHPZ1msB@C8#A9WtPOdjsHey@L>+Q5#OMJN%;Zw; 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+ "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", + "from functools import partial\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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", + "text/plain": [ + "

" + ] + }, + "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(0, 2, Nx) # the discretization in the spatial dimension is fixed\n", + " plt.subplot(3, 1, idx+1)\n", + " plt.plot(x, u0.flatten(), label=fr'$u_0(x)$')\n", + " plt.plot(x, u.flatten(), label=fr'$u(x, t=\\delta)$')\n", + " plt.xlabel(fr'$x$')\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": 21, + "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": 22, + "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", + " def forward(self, x):\n", + " t = torch.zeros(size=(x.shape[0], 1), requires_grad=False) + 0.5 # 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": 15, + "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": 16, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "💡 Tip: For seamless cloud uploads and versioning, try installing [litmodels](https://pypi.org/project/litmodels/) to enable LitModelCheckpoint, which syncs automatically with the Lightning model registry.\n", + "GPU available: True (mps), used: False\n", + "TPU available: False, using: 0 TPU cores\n", + "HPU available: False, using: 0 HPUs\n" + ] + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "89ff4d5ab3784a9bac31831e1edd263f", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "Training: | | 0/? [00:00" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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", 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FEh4e3uREEzWnPRv+i+SsqfKBY+rDexEeFgF/4LRVouRv3RGJEnwz8HVcO+42rZNE1GLErs7hcMDpdGqdFN0Sd/M0mUwXPZgS+++IiIgG7b9NjS2Y+++/H0uXLsXq1asvG1QIQUFBciDyJeWb3Pd72NFuLIb4SVAhGC3BONxxAvoeex9B2e8BDCwogIidpdlslgM1L0NjT3988MEHWLBggbyXxcmTJ+VQUVHRfCkkakHnTuehV9FaOd3u2rvhbzqP+a0cp9s2I2fPbq2TQ0SBHli88cYbshkkIyNDPhzFM3z0Ea+NJ/+wO+tfsCgO7Dd2Q1Jf9x0r/UlkxxQcDE2DUVFx7Kt/ap0cIgr0wEKcCrnYcMcddzRfColaiOpyIe7gx3L6bM/JftNpsy7jQPczT3rn/weFJWxtJCLv4rNCiKrs/PZLdHEdRYVqQcqYu+CvEodNRonSGu2VM9j4xWKtk0NEfoaBBVEV67o5cpzTbjTCItvBXynmEOQlTpDTrXI+gMvV6AvDiIguiYEFEYCTxw6gb6m702bUqAfg7zqNvk+Ohzo2Y1P2D1onh4j8CAMLIgC5n70Ck+JCTlAaOqcMhr8Lbt8LuWHpMs9Fq1/XOjlE5EcYWFDAqygrQUrev+W0Lf0eBIqQ4ffL8dCiFfjxZL7WySEiP8HAggLezs/nIQJlOK7Eos9PJiNQxKWPR56pA8KVcuz5/A2tk0NEfoKBBSHQLzGN2TVfTh/tfhuMpiY/Psf3GAwo7OO++iX5yAew2mxap4iI/AADCwpoezb8B4muYyhVQ5By4zQEmqTRd6MIrdEB+cj+YoHWySEiP8DAggKaY8M/5PiH6HGIaNMWgcYUEoZ9HSfK6bBs3omTiK4cAwsKWKcO7UDv8m/hUhXEjfb/S0wvpcuNM2BTjUix5+BQ9hqtk0NEPo6BBQWsHzNfkuNtIYPRtWcfBKqo+M7YFnGdnC5Z9YrWySEiH8fAggJS8amjSM3/j5x2Db4XgS50+O/kOPXcKpScytU6OUTkwxhYUEA6tHQWgmHHTmMK0oePR6DrlT4M24x95A2zjq54TuvkEJEPY2BBAafoxEGk5i2V0+VDH4XByM1APMm1sL/7qpgexxajLJ+tFkTUNKxRKeAcXvo0zIoT20xpGJDB1gqPa8dOxFZDb1jgwOElf9Q6OUTkoxhYUEA5e2w3UvNXyGn78CdgMChaJ0k3zCYjKoa7A4rkU5/i7GE+nIyIGo+BBQWU48uelv0INpsHYuC1Y7VOju4MGTEWGy1DYFRUnFz6pNbJISIfxMCCAkZB7naknlnpfvGTJ2W/AqpNrJPQ62fCqSpIKVqLEzu/0TpJRORjGFhQwDi5fCYMioqNQUMw4OoMrZOjW2n9r8aGsDFyuvTTPwKqqnWSiMiHMLCggHB637fyHg3iLptBo/7I1op6JIz/M6yqCUkV2TiwyX2/DyKihmBgQf7P6UDFv6fLyfUhGeg3YIjWKdK9bj2S8W27n8lpw1d/hupyap0kIvIRDCzI7x1a8Tw6WfehSA1F9M+fZ2tFA/WcOFM+9bWr4wCyP3lB6+QQkY9gYEF+zZp/AAnbXpTTqxNnILlHD62T5DNi4ztia5L74WzJO19A/pFdWieJiHwAAwvyX6qK/A/vRTBs2Kz0xsgpv9c6RT5nyKRH8IM5DSGwoXDBPTwlQkT1YmBBfuvMN2+hY9FmVKgWFI16AeEhFq2T5HNMJhPCJ81DmRqMntYd2LaEzxEhostjYEF+SS3OQ8iqmXJ6aeTtuG7IYK2T5LM6d78K25IflNNX5byEk4d2ap0kItIxBhbkf1QVpxZORyu1FDtcXXH1L3h56ZW65pZHsN3SDyGKDUWL7oHqdGidJCLSKQYW5HcKP38GcXlfwq4akd3vz+gaG6l1knye0WhA28nz5FUiPW052LpwltZJIiKdYmBBfqXo2w/R5rv/k9NzWv0WE//nRq2T5Dc6du2J7JRH5HS//a9hZ9Z8rZNERDrEwIL8Run+9Qj5/HdyeqF5An5x3x8RbDZqnSy/MnTi7/FN25/LW6MnrX8IB77L1DpJRKQzDCzIL1TmH4JzwRRY4MAqZRCG3vM6YsKCtU6W31EMBlx93zxsDhkGi+JA7Gd34sS+LVoni4h0hIEF+Tx7WSEK3pyACLUIu9AF8Xe+j07RYVony2+ZzWZcNW0RdppSEIZymBdORGFertbJIiKdYGBBPs16Ohf5L2egvf0ITqltYL15AZI7xWmdLL/XunUYYu/+BLlKB0SrBSj+13icPXlE62QRkQ4wsCCfVXpgIyreEEHFYRlUHL7hXfTrlaJ1sgJGdGw8lKmfIB9tkOg8Atfc4di2fqXWySIijTGwIJ907ruFsHxwEyJd57AbnXHi5hUYfPUIrZMVcDp364nSKf9FrqETonAOqVlT8On8Z2F18NbfRIGKgQX5FocNZ1fMRORn98ICO9YoA6H8KhP9evfSOmUBq2vP3oh/aB1yIjJgUZwYd3g2vnz+VhzIK9A6aUSkAQYW5DMqcz5D4QvpaPv9y/L1x+bx6DptKZI7xWudtIAX3CoCqTOWYX+v38MFBeOsn8M5dwSWL34XNjtbL4gCiaKqqtpSCysuLkZERASKiooQHh7eUoslH2c7tRf5ix9EhzPr5Ot8NRIfRtyN2+55BFGtg7ROHtVRmL0C5v/ci9auEvl6qzENwTf+BSnpw7VOGhG1wP6bgQXpk8uFwpwvULDuHXQ+lQUTnLCpRiyx/BRtxj6Bsf17wGDg8z/0Si0/i4OfPINOB96T9xYRtkdch/Brf4PO/UdBMfDGZUS+pNkDizlz5uD555/HyZMnkZaWhtdeew2DBg3yasIoAKkqSvP24Miq+Yg5tBTRzlPVH32jpKNg2NMYlzEMZiPP4PmK4rwD2L/ocaQXZVW/d0qJwqG46xE5+Fb07HMNA0SiQA8sPvroI/zyl7/E3LlzMXjwYLz88stYvHgx9u7di5iYGK8ljAKAwwb19B6c2bUGJXvXIvLMFrR1ne/wV6yGYkPoSLjSfoGMn1yPUItJ0+RS023fvBbFa/+BtOI1CFfKq98/rkbjUHAKzrVLAzoMRHT3AejTOYZlTRRIgYUIJgYOHIjXX39dvna5XOjYsSPuv/9+PPbYY15LGHmfKGpR2t4+QnS6VHl5ofwnqSoUlw2KvQKuyiLYi/PhKDkDZ+lpuErPwFGQC8O5XISWHkW4NQ9GuGr9ljjdscPUCwVJtyBl5BR0iGnn1bSStsrLS7F77b9h3LkEKSUb5G3BaxJPpD2OaBRa4uGKTERYXDeExXSCGtwGrpC2UEPaAsGRMIeEIzg4SD4LJshkgKIoTd4m7E4VFXYnKu3u/3B0WBCMl9hGxPzFFQ44q6pNT/XZOtiEIBNP75D/arbAwmazITQ0FEuWLMGECROq37/99ttx7tw5LF++vNb8VqtVDjUTJoIQbwcWNqsV+W/dAqfLBYdLlTs6zyByp6JqrEJWCA4xn9P9uZjfZFBk5RRkNsJiNMjXVodL7ixtDhdsThcMioJgs0FWHmJe0Rwvvmt3un9LjEXdZqn6zFz1O2IZ4jNReYmxTJeqwuVS4VIBl6rK3xb1mKjM5LQco+p9Rf6uoFbN7ykwo6LI74jBZADOV4Xu74jlWGWF6ZKVps3hlMuUcyju+Y0K5HeNBpFewGxUYKhagiL791etONUJuJyA6pJjg+qEUbXDBAfMVUMIrAiFFSaldrBwOSVqCLLVHjgZ2Q+h3YchdeBIdI6P9tp/g/TLXl6EU7s3ovTgBpjztiCmaAfCXEUN/75qRAUsqEQQrDDDqYieOCY5dikmKEYjDAYjDEYTTEajeNAJrE4RBFcNYtt1Vf29xfZVtQWJIEUELCFmoxyLbabS4Q48xLbk3gZrBx7ilfyOxYhQS9X3quoXh1yOu76R3/UsT1Wrtl0DjEYxdg/n6wCxbXt+3f0lz7Yv0iQPFOR0VV1ScxmArMssRgVmk6jX3OkV9Zqo08RY1INi2aI+E/WWmF8symp3132eeUUa3XWaeyzS5alrPfkS9Zt8z+l+T6TB8x1TVToEpwtV3xHr8fy6c6/3C8tYlIX4HZlGowKLySjncy/n/Hr1/I6Y3zOWdahnfSrn63/PvkGksS7POnRU1dFi+vxvnv/9i6XTWGd5ilJzuvb8stxcgM0p6mWx/pywOVVZp5ur8inyK9a9Z58h1p1Yb+5lna/7PetD7KfsDrGvccEBE4b/KVOzwKJR7Y1nzpyB0+lEbGxsrffF6z179lww/+zZszFr1iw0N5fqQof81U37ctU2C3vVcCliHlvVcDnn46iG8/y/m/uqPMNllu+sGi63Duqq5yDRqppRgDAUIhxFSgRKDOEotsSiIqwL1LZdYInpgdiEThjUNQqtg9j0HWjMoRHokH49IAZBVPTFx3H62F4cO7gb507sh+vsYbS2n0UESuQQiRIZvMrvK06YUYFwVNT+YXeUgDqNYY3bJjzbQ2UD50fV8iov8p1AJRqjajdIUUM4mrgfqVP3ioDkUi1vza1Za/PHH38cDz744AUtFt4WZDbj3aiHZNQtWxTM7uhbvJZRnYwYDe6jcxH9mg0INhkQbBbNlwoq7C4UV9hRXOlAcaVdRnxiRxcebEZYsEkOIhr0zFNUbpdNp56jGnGUIsaiIMttDpTZnKiwOeTRjWjlCLGY5OfiSEYs29Oa4R6Llg9XrVaNmtG4p2XFE3278yPbEdytKfLIQkSrThkB14zBxXciQi2IDDEjsmpsqToCE0c7ImJ3OlVUisHhbtUQaZYtPaIGFctR3M3MZpMJFrMJJrMZQWaLfBCVOSgYZnMQzJYgmIOCYDCHwmUOhWoOFXsNGEwWxBkNSGDnPGoIcegV0QHRYuh13aXnc9hEcwcclaWwVpbBVlEKe2U5HHabbFV12K2w222osNpQWmFDudWGskobVKcDESEmRISYERFsQkSwe9t1tzIqMCmKPEgpqrCjoNSGs2U2FJZZYTIq1dtPm1ALwoKNF1TYZVYnCkqtKCizyXFhuV1u3+L3RR0g6gpRJ3m2X0+rpKhXRAuBu0XEJe/5Ya/TElpz9Yho3tOa6W7hFPXC+dYEs2j1EK0KBneaSivtKBVjq11ux+GyPjPL+k3URxU2J0qsDpRUOlBqdUcBYp7wEHN1/SfSWG51oNzmlIPd5UKwySjrUNHK665P3a00slXXbJTrUtSRYv4ym0N+Xyzf0zLiWeeCbHCo0RojeNplRZ0m0iWHqryIo3a5LLlMg6zT5PGhqM+qWnU9rRKeVmJRt4r1FSTWUVULjVx/df5acv9gcrfyiHlF2XtaOuTY08xSJ62iHpX1eFWd7fC0motyrEpPVSlWf0/kX5SDZwgNMsLuUGVexTorszpkHS/XmWe9GQ0yj6K+F60Tou4X3RHE/6xVkAmtLCa0CjIiNDgIl+/xqKPAIioqCkajEadOne+tL4jXcXEXPvgpKChIDs1NMZpw+/Snmn05RKQDJoscTCGRsgJr5cWfFjuaNlVDY4RVDZ29mBYiX9Wo6/YsFgvS09Px1VdfVb8noiXx+pprrmmO9BEREZEPafSpEHFqQ3TWHDBggLx3hbjctKysDHfeeWfzpJCIiIj8N7CYNGkSTp8+jaeeekreIKtv377IzMy8oEPnxXguQBF9LYiIiMg3ePbbDbmQtEVv6f3jjz82S+dNIiIian7Hjh1Dhw4d9BNYiP4YJ06cQFhYWJNvaHMpnitORKb98eZb/p6/QMgj8+f7/D2P/p6/QMhjcTPlT4QKJSUlSEhIkFciXU6L3jxAJKa+SOdKiRXpj3+WQMlfIOSR+fN9/p5Hf89fIOQxvBnyJ26Q1RB8mhMRERF5DQMLIiIi8hq/CSzEjbhmzpzZIjfk0oK/5y8Q8sj8+T5/z6O/5y8Q8hikg/y1aOdNIiIi8m9+02JBRERE2mNgQURERF7DwIKIiIgCI7CYM2cOOnfujODgYAwePBjffffdZedfvHgxkpOT5fy9e/fGZ599Vutz0Z1E3Io8Pj4eISEhGDVqFPbv3w9fyN+bb76Ja6+9Fm3atJGDSHvd+e+44w5547Gaw/XXXw9fyN/8+fMvSLv4np7Lr7F5zMjIuCCPYhg3bpwuy3Dt2rW46aab5A1xRDqWLVtW73dWr16N/v37y45j3bt3l+V6pdu1XvL3ySefYPTo0YiOjpb3BxAPXly5cmWteZ5++ukLyk/USb6QP1F2F/t/ikc36LH8mpLHi21fYkhNTdVlGc6ePRsDBw6UN5WMiYnBhAkTsHfv3nq/p/W+ULeBxUcffSQfeCZ6t27duhVpaWkYO3Ys8vPzLzr/hg0bMGXKFNx1113Ytm2bLAAx7Ny5s3qev//973j11Vcxd+5cfPvtt2jVqpX8zcrKSug9f2KjF/lbtWoVNm7cKO+sNmbMGBw/frzWfGInlJeXVz0sXLgQWmhs/gRRWddM+5EjR2p9rqfya0oexY6pZv7Ef9NoNGLixIm6LEPxcEGRJ7EjaYjc3FwZJI0cORLZ2dmYMWMGfv3rX9fa+Tblf6GX/ImdmAgsRCW9ZcsWmU+xUxP1TU1iJ1Wz/NatWwctNDZ/HmLHVTP9Yoemx/JrSh5feeWVWnkTd6ds27btBdugXspwzZo1mDZtGjZt2oQvvvgCdrtd1vsi35eii32hqlODBg1Sp02bVv3a6XSqCQkJ6uzZsy86/y233KKOGzeu1nuDBw9Wf/Ob38hpl8ulxsXFqc8//3z15+fOnVODgoLUhQsXqnrPX10Oh0MNCwtT33333er3br/9dnX8+PGqHjQ2f++8844aERFxyd/TW/l5owxfeuklWYalpaW6LMOaRFWxdOnSy87zhz/8QU1NTa313qRJk9SxY8d6bZ1pmb+LSUlJUWfNmlX9eubMmWpaWpqqNw3J36pVq+R8hYWFl5xHr+XX1DIU8yuKoh4+fFj3ZSjk5+fLfK5Zs0a9FD3sC3XZYmGz2eQRgWieqXk7cPFaHK1fjHi/5vyCiMA884ujKdGkV3MecXtS0ZR3qd/UU/7qKi8vl9GriLbrtmyII4yePXvivvvuQ0FBAVpaU/NXWlqKxMRE2Rozfvx45OTkVH+mp/LzVhm+9dZbmDx5sjxa0FsZNkV926A31pmeiGcfiWcn1N0GRZOyaJrv2rUrbr31Vhw9ehS+RDyxWjSRi9aZ9evXV7/vb+Xn2QZF+kW94wtlWFRUJMd1/3N62xfqMrA4c+YMnE7nBY9iF6/rnu/zEO9fbn7PuDG/qaf81fXoo4/KP37NP4doQn/vvffw1Vdf4bnnnpPNaDfccINclt7zJ3aib7/9NpYvX44PPvhAVtpDhgyRT8TVW/l5owzFeWnRNClOFdSklzJsikttg+KhSBUVFV753+vJCy+8IIPhW265pfo9UTmLfiWZmZl44403ZCUu+kaJAETvRDAhmsb//e9/y0EE+KJfkDjlIfhb+YkHYn7++ecXbIN6LUOXyyVPLw4dOhS9evW65Hx62Be26EPIyDueffZZLFq0SB7Z1uzgKI5+PUSHnT59+qBbt25yvuuuuw56JjrCicFDBBVXXXUV5s2bh2eeeQb+RhwpiTIaNGhQrfd9uQwDyYIFCzBr1iwZCNfsgyCCQA9RdmInJY6GP/74Y3nOW89EcC+GmtvgwYMH8dJLL+H999+Hv3n33XcRGRkp+x/UpNcynDZtmjwY0aq/h8+3WERFRclObadOnar1vngdFxd30e+I9y83v2fcmN/UU/5qHiWJwCIrK0v+6S9HNOOJZR04cAC+kj8Ps9mMfv36VaddT+V3pXkUHa9EYNiQSkqrMmyKS22DolOu6Hnujf+FHoiyE0e5YkdTt8m5LrHjSkpK8onyuxgR+HrS7i/lJ4guGaKF9LbbboPFYtF9GU6fPh0rVqyQnffre0K4HvaFugwsREGnp6fL5uCazUDidc2j2prE+zXnF0QvWs/8Xbp0kSut5jyiiVb0iL3Ub+opf56evOLoXTTRDRgwoN7liNMI4vy8aOL0hfzVJJpcd+zYUZ12PZXfleZRXApmtVoxdepU3ZZhU9S3DXrjf6E1cYXOnXfeKcc1LxO+FHGqRBz1+0L5XYy4useTdn8oPw9xilEECg0J7rUsQxEAiaBi6dKl+Prrr2U9WB9d7AtVnVq0aJHspTp//nx1165d6j333KNGRkaqJ0+elJ/fdttt6mOPPVY9//r161WTyaS+8MIL6u7du2XPXrPZrO7YsaN6nmeffVb+xvLly9UffvhB9r7v0qWLWlFRofv8ibRbLBZ1yZIlal5eXvVQUlIiPxfjhx9+WN24caOam5urfvnll2r//v3VHj16qJWVlbrPn+hZv3LlSvXgwYPqli1b1MmTJ6vBwcFqTk6OLsuvKXn0GDZsmLxaoi69laFIz7Zt2+QgqooXX3xRTh85ckR+LvIm8uhx6NAhNTQ0VH3kkUfkNjhnzhzVaDSqmZmZDV5nes7fhx9+KOsYka+a26DoUe/x0EMPqatXr5blJ+qkUaNGqVFRUbI3v97zJ65SWrZsmbp//35Zbz7wwAOqwWCQ/0M9ll9T8ugxdepUeaXExeipDO+77z55tZxIT83/XHl5efU8etwX6jawEF577TW1U6dOcocqLnPatGlT9WcjRoyQl+bV9PHHH6tJSUlyfnHZ26efflrrc3GZzZ/+9Cc1NjZWbhzXXXedunfvXtUX8peYmCg3nLqD+NMI4o82ZswYNTo6Wv6JxPx33323Zht8Y/M3Y8aM6nlF+dx4443q1q1bdV1+TfmP7tmzR5ZbVlbWBb+ltzL0XH5Yd/DkSYxFHut+p2/fvnJ9dO3aVV5G3Jh1puf8ienLzS+IgDE+Pl7mrX379vL1gQMHfCJ/zz33nNqtWzcZ0Ldt21bNyMhQv/76a92WX1P/oyIQDAkJUf/5z39e9Df1VIa4SN7EUHO70uO+kE83JSIiIq/RZR8LIiIi8k0MLIiIiMhrGFgQERGR1zCwICIiIq9hYEFERERew8CCiIiIvIaBBREREXkNAwsiIiLyGgYWRERE5DUMLIiIiMhrGFgQERGR1zCwIKIrIh4hHhISgry8vOr3xKPF+/Tpg6KiIk3TRkQtjw8hI6IrIqqQvn37Yvjw4Xjttdcwc+ZMvP3229i0aRPat2+vdfKIqIWZWnqBRORfFEXBX//6V9x8882Ii4uTwcU333zDoIIoQLHFgoi8on///sjJyUFWVhZGjBihdXKISCPsY0FEVywzMxN79uyB0+lEbGys1skhIg2xxYKIrsjWrVuRkZGBefPmYf78+QgPD8fixYu1ThYRaYR9LIioyQ4fPoxx48bhiSeewJQpU9C1a1dcc801MtgQp0aIKPCwxYKImuTs2bMYMmSIbK2YO3du9fsi0BCnRMTpESIKPAwsiIiIyGvYeZOIiIi8hoEFEREReQ0DCyIiIvIaBhZERETkNQwsiIiIyGsYWBAREZHXMLAgIiIir2FgQURERF7DwIKIiIi8hoEFEREReQ0DCyIiIvIaBhZEREQEb/l/Eb/bN6FZL1MAAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "for i in [1, 2, 3]:\n", + " plt.subplot(3, 1, i)\n", + " plt.plot(torch.linspace(0, 2, Nx), solver(data_0_training)[10*i].detach().flatten(), label=r'$u_{NN}$')\n", + " plt.plot(torch.linspace(0, 2, Nx), data_dt_training[10*i].extract('u').flatten(), label=r'$u$')\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": 25, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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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(torch.linspace(0, 2, Nx), data_dt_training[10*i].extract('u').flatten() - solver(data_0_training)[10*i].detach().flatten(), label=r'$u - u_{NN}$')\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": "pina", + "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": "3.10.18" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +}

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