PINA: A PyTorch Framework for Solving Differential Equations by Deep Learning for Research and Production Environments

Abstract

We present a versatile software designed for solving differential equations employing neural networks. The package is called PINA, an open-source Python library built upon the robust foundations of PyTorch and Lightning. It allows end-users to formulate their problem and craft their models to effortlessly compute solutions of PDEs by Physics Informed Neural Networks and Neural Operators. The modular structure of PINA permits it to adapt for user specifics, thus offering the freedom to select the most suitable learning techniques for their particular problem domain. Furthermore, by leveraging the capabilities of the Lightning package, PINA adapts to various hardware setups, including GPUs and TPUs. This adaptability positions PINA as an ideal candidate for the transition of these methodologies into production and industrial pipelines, where computational efficiency and scalability are of paramount importance.