Title: Multiphysics Bench: Benchmarking and Investigating Scientific Machine Learning for Multiphysics PDEs
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
Keywords: Multiphysics, PDEs, Benchmark, Scientific Machine Learning

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. For example, in 3D integrated circuits (ICs), electrical current injection or electromagnetic wave propagation can induce localized heating, which in turn alters the electromagnetic properties of the embedded components. 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 field quantities, thereby introducing additional complexity and challenges, such as inter-field coupling. Nevertheless, benchmark testing for the application of machine learning in solving multiphysics problems 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, which focuses on multiphysics PDE solving with machine learning. Multiphysics Bench is also the most comprehensive multiphysics PDE dataset to date, featuring the broadest range of coupling types, the greatest diversity of multiphysics PDE formulations, and the largest scale of coupled physics data. Second, we conduct the first systematic investigation on multiple representative learning-based PDE solvers, such as Physics-Informed Neural Networks (PINNs), Fourier Neural Operators (FNO), Deep Operator Networks (DeepONet), DiffusionPDE and M2PDE solvers, on multiphysics problems. Unfortunately, naively applying these existing solvers usually shows 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. Notably, our multiphysics data enables PDE solvers to incorporate more comprehensive physical laws, leading to more accurate solutions to real-world problems.

TL;DR: We present the Multiphysics Bench, the first comprehensive benchmark for evaluating machine learning solvers for multiphysics PDEs, revealing key limitations of existing models while providing actionable insights and tools for future advances.