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 often rely on numerical solvers or machine learning-based surrogate models to solve or accelerate these simulations. However, multiphysics simulations typically require integrating multiple specialized solvers-each responsible for evolving a specific physical process-into a coupled program, which introduces significant development challenges. Furthermore, no universal algorithm exists for multi-component simulations, which adds to the complexity. Here we propose compositional Multiphysics and Multi-component Simulation with Diffusion models (MultiSimDiff) to overcome these challenges. During diffusion-based training, MultiSimDiff learns energy functions modeling the conditional probability of one physical process/component conditioned on other processes/components. In inference, MultiSimDiff generates coupled multiphysics solutions and multi-component structures by sampling from the joint probability distribution, achieved by composing the learned energy functions in a structured way. We test our method in three tasks. In the reaction-diffusion and nuclear thermal coupling problems, MultiSimDiff successfully predicts the coupling solution using decoupled data, while the surrogate model fails in the more complex second problem. For the thermal and mechanical analysis of the prismatic fuel element, MultiSimDiff trained for single component prediction accurately predicts a larger structure with 64 components, reducing the relative error by 40.3% compared to the surrogate model.

翻译：多物理场仿真（模拟多个物理过程之间的相互作用）与复杂结构的多组件仿真在核能与航空航天工程等领域至关重要。先前研究通常依赖数值求解器或基于机器学习的代理模型来解决或加速此类仿真。然而，多物理场仿真通常需要将多个专用求解器（各自负责演化特定物理过程）集成到耦合程序中，这带来了巨大的开发挑战。此外，多组件仿真缺乏通用算法，进一步增加了复杂性。本文提出基于扩散模型的组合式多物理场与多组件仿真方法（MultiSimDiff）以应对这些挑战。在基于扩散的训练过程中，MultiSimDiff学习能量函数，该函数建模一个物理过程/组件在其他过程/组件条件下的条件概率。在推理阶段，MultiSimDiff通过从联合概率分布中采样生成耦合的多物理解与多组件结构，这是通过以结构化方式组合已学习的能量函数实现的。我们在三个任务中测试了所提方法。在反应-扩散与核热耦合问题中，MultiSimDiff成功利用解耦数据预测耦合解，而代理模型在更复杂的第二个问题上失效。对于棱柱形燃料元件的热力学与机械分析，针对单组件预测训练的MultiSimDiff能够准确预测包含64个组件的更大结构，相较于代理模型将相对误差降低了40.3%。