M2PDE: Compositional Generative Multiphysics and Multi-component PDE Simulation
This addresses simulation bottlenecks in fields like nuclear and aerospace engineering, offering a novel method for complex, large-scale problems.
The paper tackles the challenges of multiphysics and multi-component simulations by proposing M2PDE, a diffusion model that learns energy functions for conditional probabilities and generates coupled solutions, achieving more accurate predictions than surrogate models in tasks like reaction-diffusion and nuclear thermal coupling, and outperforming existing approaches in scaling to a 64-component structure.
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.