ECCOMAS 2024

PINA: a PyTorch Framework for Deep Differential Equation Learning for Research and Production Environments

  • Coscia, Dario (SISSA mathLab)
  • Demo, Nicola (Fast Computing)
  • Rozza, Gianluigi (SISSA mathLab)

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The last years have seen a growing interest within the scientific computing community to exploit machine learning to address the limitations of conventional methods for solving differential equations. Physics-informed neural network (PINN) and Neural Operator (NO) approaches have emerged as central players due to their promising and innovative approaches to computing differential equations’ solutions. In this contribution, we will present a versatile software designed for tackling differential equation learning using PINN and NO methodologies. The package is called PINA, and it is an open-source Python library built upon the robust foundations of PyTorch and PyTorchLightning. It empowers end-users to formulate their problem and craft their models to compute the solution effortlessly. The modular structure of PINA permits it to adapt PINN and NO schemas 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 PyTorchLightning package, PINA makes possible the usage of state-of-the-art features for machine learning in the PINN and NO context and adapts to various hardware setups, including GPUs and TPUs. This adaptability makes PINA an ideal candidate for the transition of these methodologies into production and industrial pipelines, where computational efficiency and scalability are of fundamental importance. The contribution will summarize the basic concepts of both methodologies, presenting the package structure to conclude with the solutions of benchmark problems using PINA