Multiphysics Bench: Benchmarking and Investigating Scientific Machine Learning for Multiphysics PDEs

TL;DR

This paper introduces a comprehensive multiphysics PDE dataset, evaluates existing machine learning solvers on multiphysics problems, and provides insights and techniques to improve their performance in complex coupled systems.

Contribution

It presents the first multiphysics dataset, systematically investigates existing ML PDE solvers on these problems, and offers practical insights and tricks for better solutions.

Findings

Naive application of existing solvers performs poorly on multiphysics problems.

The Multiphysics Bench dataset is the most comprehensive to date.

Several useful techniques are identified to enhance multiphysics PDE solving with ML.

Abstract

Solving partial differential equations (PDEs) with machine learning has recently attracted great attention, as PDEs are fundamental tools for modeling real-world systems that range from fundamental physical science to advanced engineering disciplines. Most real-world physical systems across various disciplines are actually involved in multiple coupled physical fields rather than a single field. However, previous machine learning studies mainly focused on solving single-field problems, but overlooked the importance and characteristics of multiphysics problems in real world. Multiphysics PDEs typically entail multiple strongly coupled variables, thereby introducing additional complexity and challenges, such as inter-field coupling. Both benchmarking and solving multiphysics problems with machine learning remain largely unexamined. To identify and address the emerging challenges in multiphysics problems, we mainly made three contributions in this work. First, we collect the first general multiphysics dataset, the Multiphysics Bench, that focuses on multiphysics PDE solving with machine learning. Multiphysics Bench is also the most comprehensive PDE dataset to date, featuring the broadest range of coupling types, the greatest diversity of PDE formulations, and the largest dataset scale. Second, we conduct the first systematic investigation on multiple representative learning-based PDE solvers, such as PINNs, FNO, DeepONet, and DiffusionPDE solvers, on multiphysics problems. Unfortunately, naively applying these existing solvers usually show very poor performance for solving multiphysics. Third, through extensive experiments and discussions, we report multiple insights and a bag of useful tricks for solving multiphysics with machine learning, motivating future directions in the study and simulation of complex, coupled physical systems.