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

2025-05-23

AI Summary

Existing machine learning solvers—such as PINNs, FNOs, and DeepONets—excel on single-field PDEs but lack systematic evaluation and methodological adaptation for strongly coupled multiphysics systems governed by multi-physics PDEs. To address this gap, we introduce Multiphysics Bench, the first general-purpose benchmark dataset for strongly coupled multiphysics PDEs, comprising 12 canonical problem classes. Through rigorous evaluation, we identify a critical failure mode: mainstream methods suffer significant performance degradation due to inadequate modeling of inter-field coupling. We propose three targeted strategies—loss reweighting, gradient coordination, and cross-field information interaction—to mitigate this limitation. Our experiments deliver reproducible baselines, failure-mode analysis, and 12 actionable guidelines. This work establishes the first comprehensive benchmark and methodology framework for multiphysics scientific machine learning, bridging the gap between current solvers and real-world complex physical systems.

Technology Category

• Machine Learning: Multimodal Learning
• Multiagent Systems: Distributed Problem Solving
• Natural Language Processing: Language Grounding & Multi-modal NLP

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Benchmarking machine learning for multiphysics PDE solving
• Investigating challenges in coupled physical field modeling
• Developing insights for multiphysics solver performance improvement

Innovation

• Developed first general multiphysics dataset
• Systematically tested learning-based PDE solvers
• Provided insights for multiphysics machine learning