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| .. docmeta:: | ||
| :last_reviewed: 2026-06-24 | ||
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| License | ||
| ============== | ||
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| .. docmeta:: | ||
| :last_reviewed: 2026-06-24 | ||
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| Cite PINA | ||
| ============== | ||
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| .. docmeta:: | ||
| :last_reviewed: 2026-06-24 | ||
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| Installation | ||
| ============ | ||
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| **PINA** requires requires `torch`, `lightning`, `torch_geometric` and `matplotlib`. | ||
| **PINA** requires `torch`, `lightning`, `torch_geometric` and `matplotlib`. | ||
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| Installing via PIP | ||
| __________________ | ||
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| Mac and Linux users can install pre-built binary packages using pip. | ||
| To install the package just type: | ||
| Mac and Linux users can install pre-built binary packages using pip: | ||
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| .. code-block:: bash | ||
| $ pip install pina-mathlab | ||
| pip install pina-mathlab | ||
| To uninstall the package: | ||
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| .. code-block:: bash | ||
| $ pip uninstall pina-mathlab | ||
| pip uninstall pina-mathlab | ||
| Installing from source | ||
| ______________________ | ||
| The official distribution is on GitHub, and you can clone the repository using | ||
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| .. code-block:: bash | ||
| $ git clone https://github.com/mathLab/PINA | ||
| The official distribution is on GitHub. Clone the repository: | ||
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| To install the package just type: | ||
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| .. code-block:: bash | ||
| $ pip install -e . | ||
| git clone https://github.com/mathLab/PINA | ||
| Then install in editable mode: | ||
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| .. code-block:: bash | ||
| pip install -e . | ||
| Install with extra packages | ||
| ____________________________ | ||
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| To install extra dependencies required to run tests or tutorials directories, please use the following command: | ||
| To install extra dependencies required to run tests or tutorials, use: | ||
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| .. code-block:: bash | ||
| $ pip install "pina-mathlab[extras]" | ||
| pip install "pina-mathlab[extras]" | ||
| Available extras include: | ||
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| * `dev` for development purpuses, use this if you want to Contribute. | ||
| * `test` for running test locally. | ||
| * `doc` for building documentation locally. | ||
| * `tutorial` for running tutorials | ||
| * ``dev`` — development tools (use this if you want to contribute). | ||
| * ``test`` — for running tests locally. | ||
| * ``doc`` — for building the documentation locally. | ||
| * ``tutorial`` — for running tutorials. | ||
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| Requirements | ||
| ____________ | ||
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| PINA is built on: | ||
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| * `PyTorch <https://pytorch.org/>`_ — deep learning framework. | ||
| * `PyTorch Lightning <https://lightning.ai/docs/pytorch/stable/>`_ — training loop orchestration. | ||
| * `PyTorch Geometric <https://pytorch-geometric.readthedocs.io/en/latest/>`_ — graph neural network support. | ||
| * `Matplotlib <https://matplotlib.org/>`_ — plotting and visualisation. | ||
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| See Also | ||
| -------- | ||
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| * :doc:`Quickstart guide <_quickstart>` | ||
| * :doc:`API Reference <_rst/_code>` |
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| .. docmeta:: | ||
| :last_reviewed: 2026-06-24 | ||
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| Quickstart | ||
| ========== | ||
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| This guide gets you up and running with PINA in 5 minutes. By the end, you will have trained a Physics-Informed Neural Network (PINN) to solve the Poisson equation on a unit square. | ||
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| Install | ||
| ------- | ||
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| .. code-block:: bash | ||
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| pip install pina-mathlab | ||
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| Define a problem | ||
| ---------------- | ||
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| Every PINA workflow starts by defining a :class:`~pina.problem.spatial_problem.SpatialProblem`. | ||
| A problem specifies the output variables, the computational domain, and the conditions | ||
| (PDE residual, boundary conditions, initial conditions, data) that the solver must satisfy. | ||
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| .. code-block:: python | ||
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| from pina import Condition | ||
| from pina.problem import SpatialProblem | ||
| from pina.domain import CartesianDomain | ||
| from pina.equation import Equation, FixedValue | ||
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| class PoissonProblem(SpatialProblem): | ||
| output_variables = ["u"] | ||
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| domains = { | ||
| "domain": CartesianDomain({"x": [0, 1], "y": [0, 1]}), | ||
| "boundary": CartesianDomain({"x": [0, 1], "y": [0, 1]}), | ||
| } | ||
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| conditions = { | ||
| "domain": Condition( | ||
| domain="domain", | ||
| equation=Equation("d2(u,x) + d2(u,y) + sin(pi*x)*sin(pi*y) = 0"), | ||
| ), | ||
| "boundary": Condition( | ||
| domain="boundary", | ||
| equation=FixedValue(0.0), | ||
| ), | ||
| } | ||
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| problem = PoissonProblem() | ||
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| Create a model | ||
| -------------- | ||
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| Choose a neural network architecture. For standard PINNs, a :class:`~pina.model.feed_forward.FeedForward` (MLP) is a solid starting point. | ||
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| .. code-block:: python | ||
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| from pina.model import FeedForward | ||
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| model = FeedForward( | ||
| input_dimensions=2, | ||
| output_dimensions=1, | ||
| inner_size=20, | ||
| n_layers=3, | ||
| ) | ||
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| Train with a solver | ||
| ------------------- | ||
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| The :class:`~pina.solver.physics_informed_solver.pinn.PINN` solver wraps the problem and model, and the :class:`~pina._src.core.trainer.Trainer` orchestrates the training loop. | ||
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| .. code-block:: python | ||
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| from pina.solver import PINN | ||
| from pina import Trainer | ||
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| pinn = PINN(problem=problem, model=model) | ||
| trainer = Trainer(solver=pinn, max_epochs=1000) | ||
| trainer.train() | ||
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| Inspect results | ||
| --------------- | ||
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| After training, the model stores its solution in the solver. Evaluate at any point: | ||
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| .. code-block:: python | ||
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| import torch | ||
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| x = torch.tensor([[0.5, 0.5]], requires_grad=True) | ||
| u_pred = pinn(x) | ||
| print(u_pred) | ||
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| What's next? | ||
| ------------ | ||
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| * Walk through the `Introductory Tutorial <tutorial17/tutorial.html>`_ for a deeper introduction. | ||
| * Explore the :doc:`API reference </_rst/_code>` for all available components. | ||
| * Read the :doc:`tutorials </_tutorial>` for domain-specific guides (Neural Operators, Supervised Learning, etc.). |
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