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Nicola Demo
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Welcome to PINA's documentation!
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===================================================
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:html_theme.sidebar_secondary.remove:
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Physics Informed Neural network for Advanced modeling (**PINA**) is
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an open-source Python library providing an intuitive interface for
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solving differential equations using PINNs, NOs or both together.
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Based on `PyTorch <https://pytorch.org/>`_ and `PyTorchLightning <https://lightning.ai/docs/pytorch/stable/>`_,
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PINA offers a simple and intuitive way to formalize a specific (differential) problem
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and solve it using neural networks . The approximated solution of a differential equation
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can be implemented using PINA in a few lines of code thanks to the intuitive and user-friendly interface.
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Welcome to PINA’s documentation!
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=======================================
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`PyTorchLightning <https://lightning.ai/docs/pytorch/stable/>`_ as backhand is done to offer
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professional AI researchers and machine learning engineers the possibility of using advancement
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training strategies provided by the library, such as multiple device training, modern model compression techniques,
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gradient accumulation, and so on. In addition, it provides the possibility to add arbitrary
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self-contained routines (callbacks) to the training for easy extensions without the need to touch the
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underlying code.
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.. grid:: 6
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:gutter: 1
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The high-level structure of the package is depicted in our API. The pipeline to solve differential equations
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with PINA follows just five steps: problem definition, model selection, data generation, solver selection, and training.
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.. grid-item::
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.. figure:: index_files/API_color.png
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:alt: PINA application program interface
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:align: center
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:width: 600
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.. image:: index_files/tutorial_13_3.png
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:target: _rst/tutorials/tutorial2/tutorial.html
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.. grid-item::
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Physics-informed neural network
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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.. image:: index_files/tutorial_32_0.png
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:target: _rst/tutorials/tutorial4/tutorial.html
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`PINN <https://www.sciencedirect.com/science/article/abs/pii/S0021999118307125>`_ is a novel approach that
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involves neural networks to solve differential equations in an unsupervised manner, while respecting
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any given law of physics described by general differential equations. Proposed in "*Physics-informed neural
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networks: A deep learning framework for solving forward and inverse problems
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involving nonlinear partial differential equations*", such framework aims to
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solve problems in a continuous and nonlinear settings.
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.. grid-item::
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Neural operator learning
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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.. image:: index_files/tutorial_13_01.png
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:target: _rst/tutorials/tutorial9/tutorial.html
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`Neural Operators <https://www.jmlr.org/papers/v24/21-1524.html>`_ is a novel approach involving neural networks
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to learn differential operators using supervised learning strategies. By learning the differential operator, the
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neural network is able to generalize across different instances of the differential equations (e.g. different forcing
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terms), without the need of re-training.
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.. grid-item::
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.. image:: index_files/tutorial_5_0.png
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:target: _rst/tutorials/tutorial10/tutorial.html
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.. grid-item::
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.. image:: index_files/tutorial_36_0.png
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:target: _rst/tutorials/tutorial6/tutorial.html
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.. grid-item::
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.. image:: index_files/tutorial_15_0.png
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:target: _rst/tutorials/tutorial13/tutorial.html
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.. grid:: 1 1 3 3
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.. grid-item::
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:columns: 12 12 6 6
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Physics Informed Neural network for Advanced modeling (**PINA**) is
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an open-source Python library providing an intuitive interface for
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solving differential equations using PINNs, NOs or both together.
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Based on `PyTorch <https://pytorch.org/>`_ and `PyTorchLightning <https://lightning.ai/docs/pytorch/stable/>`_, **PINA** offers a simple and intuitive way to formalize a specific (differential) problem
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and solve it using neural networks . The approximated solution of a differential equation
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can be implemented using PINA in a few lines of code thanks to the intuitive and user-friendly interface.
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Contact us by email for further information or questions about **PINA**, or suggest pull requests.
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.. toctree::
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:maxdepth: 1
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:caption: Package Documentation:
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API <_rst/_code>
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.. grid-item-card:: Contents
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:class-title: sd-fs-5
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:class-body: sd-pl-4
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.. the following is demo content intended to showcase some of the features you can invoke in reStructuredText
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.. this can be safely deleted or commented out
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.. ........................................................................................
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.. toctree::
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:maxdepth: 1
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.. toctree::
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:maxdepth: 1
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:caption: Getting Started:
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Installing <_rst/_installation>
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Tutorial <_rst/_tutorial>
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API <_rst/_code>
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Installation <_rst/_installation>
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Tutorials <_rst/_tutorial>
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.. .. grid-item-card:: Features
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.. :columns: 12 12 4 4
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.. :class-title: sd-fs-5
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.. :class-body: sd-pl-3
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.. toctree::
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:maxdepth: 1
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:caption: Community:
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Team & Fundings <_team.rst>
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Contributing <_rst/_contributing>
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License <_LICENSE.rst>
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Cite PINA <_cite.rst>
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.. * :bdg-secondary:`New` Objects: :ref:`API <objects_api>` | :doc:`Tutorial <tutorial/objects_interface>`
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.. * Relational plots: :ref:`API <relational_api>` | :doc:`Tutorial <tutorial/relational>`
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.. * Distribution plots: :ref:`API <distribution_api>` | :doc:`Tutorial <tutorial/distributions>`
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.. * Categorical plots: :ref:`API <categorical_api>` | :doc:`Tutorial <tutorial/categorical>`
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.. * Regression plots: :ref:`API <regression_api>` | :doc:`Tutorial <tutorial/regression>`
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.. * Multi-plot grids: :ref:`API <grid_api>` | :doc:`Tutorial <tutorial/axis_grids>`
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.. * Figure theming: :ref:`API <style_api>` | :doc:`Tutorial <tutorial/aesthetics>`
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.. * Color palettes: :ref:`API <palette_api>` | :doc:`Tutorial <tutorial/color_palettes>`
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