M2PDE: Compositional Generative Multiphysics and Multi-component PDE Simulation

TL;DR

M2PDE introduces a diffusion-based generative approach for coupled multiphysics and multi-component PDE simulations, enabling scalable, accurate modeling of complex structures and interactions in engineering applications.

Contribution

The paper presents a novel diffusion model framework for multiphysics and multi-component PDE simulation, overcoming integration and scalability challenges of traditional methods.

Findings

Achieves more accurate predictions than surrogate models in multiphysics tasks.

Successfully scales from single-component to 64-component simulations.

Outperforms existing domain-decomposition and graph-based approaches.

Abstract

Multiphysics simulation, which models the interactions between multiple physical processes, and multi-component simulation of complex structures are critical in fields like nuclear and aerospace engineering. Previous studies use numerical solvers or ML-based surrogate models for these simulations. However, multiphysics simulations typically require integrating multiple specialized solvers-each for a specific physical process-into a coupled program, which introduces significant development challenges. Furthermore, existing numerical algorithms struggle with highly complex large-scale structures in multi-component simulations. Here we propose compositional Multiphysics and Multi-component PDE Simulation with Diffusion models (M2PDE) to overcome these challenges. During diffusion-based training, M2PDE learns energy functions modeling the conditional probability of one physical process/component conditioned on other processes/components. In inference, M2PDE generates coupled multiphysics and multi-component solutions by sampling from the joint probability distribution. We evaluate M2PDE on two multiphysics tasks-reaction-diffusion and nuclear thermal coupling-where it achieves more accurate predictions than surrogate models in challenging scenarios. We then apply it to a multi-component prismatic fuel element problem, demonstrating that M2PDE scales from single-component training to a 64-component structure and outperforms existing domain-decomposition and graph-based approaches. The code is available at https://github.com/AI4Science-WestlakeU/M2PDE.