用扩散模型统一生成多物理场与多组件的复杂仿真,突破传统求解器局限。
M2PDE: Compositional Generative Multiphysics and Multi-component PDE Simulation
- 基于扩散模型学习各物理过程间的条件能量函数,实现联合概率采样。
- 在反应-扩散与核热耦合任务中,预测精度优于传统代理模型。
- 可从单组件训练扩展至64组件结构,适合复杂工程系统仿真。
多物理场仿真(建模多个物理过程交互)和复杂结构多组分仿真在核能、航空航天等领域至关重要。以往研究依赖数值求解器或基于机器学习的代理模型,但多物理场需集成多个专用求解器,开发难度大;现有算法在大规模复杂结构上表现受限。本文提出基于扩散模型的组合式多物理场与多组分偏微分方程仿真方法(M2PDE)。训练阶段,M2PDE学习描述一个物理过程/组分在其他过程/组分条件下的能量函数;推理时,通过联合概率分布采样生成耦合解。我们在反应-扩散与核热耦合两个多物理场任务上验证,M2PDE在挑战性场景下预测更准确。进一步应用于六十四组件棱柱形燃料元件问题,证明其可由单组件训练扩展至大规模结构,性能优于领域分解与图基方法。代码已开源:https://github.com/AI4Science-WestlakeU/M2PDE。
原文摘要 · Abstract (English)
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.
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