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

TL;DR

This work addresses the lack of standardized benchmarks for machine learning solvers of multiphysics PDEs by introducing Multiphysics Bench, a comprehensive, large-scale dataset spanning six canonical coupled problems. It provides the first systematic evaluation of four prominent SciML architectures—PINNs, DeepONet, FNO, and DiffusionPDE—on multiphysics tasks and reveals that naive single-physics applications underperform in coupled settings. The authors also present practical insights, including normalization and loss-balancing tricks, to improve robustness and generalization across interdependent physical fields. By releasing both data and code, the paper establishes a foundation for future physics-informed, scalable modeling of complex multiphysics systems with broad scientific and engineering impact.

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.

Figures (17)

• Figure 1: Illustration of the dataset collection process for the six multiphysics problems in the Multiphysics Bench. Each problem is abstracted from real-world physical phenomena, where the underlying PDEs and their coupling mechanisms are extracted and solved using FEM. Each subproblem involves the interaction between two coupled physical fields. Golden arrows indicate equation-level coupling, while pink arrows denote coupling via constitutive parameters.
• Figure 2: Performance comparisons of different frameworks on benchmark multiphysics problems. (a) Electro-Thermal Coupling, (b) Thermo-Fluid Coupling, (c) Electro-Fluid Coupling, (d) Magneto-Hydrodynamic Coupling, (e) Acoustic–Structure Coupling and (f) Mass Transport–Fluid Coupling.
• Figure 3: Simulation model for electro-thermal coupling. (a) Electromagnetic field model; (b) Thermal conduction model.
• Figure 4: Simulation model for Thermo-Fluid coupling. (a) Fluid flow model; (b) Heat transfer model.
• Figure 5: Simulation model for Electro-Fluid coupling. (a) Electrical model; (b) Fluid dynamics model.