M2PDE: Compositional Generative Multiphysics and Multi-component PDE Simulation

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 github.com/AI4Science-WestlakeU/M2PDE.

Complex simulations involving multiple interacting physical processes (like in nuclear or aerospace engineering) and large structures with many components are difficult. Existing methods either require integrating many different specialized simulation programs, which is hard to develop, or struggle with the complexity of large, multi-component structures. We develop a new method called M2PDE, which uses diffusion models to simulate these complex systems. M2PDE learns how different physical processes or components interact. During training, M2PDE learns how one physical process/component influenced on other processes/components. During the inference, it generates solutions by considering the combined probabilities of all the interactions. 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. M2PDE provides a novel and important approach for addressing complex multiphysics and multi-component PDE simulations, which is crucial across a wide range of scientific and engineering disciplines. The code is available at github.com/AI4Science-WestlakeU/M2PDE.