发表机构
Worcester Polytechnic Institute; Sandia National Laboratories（伍斯特理工学院; 桑迪亚国家实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于强化学习的在线自适应混合区域分解方法，通过深度Q网络动态选择FOM或ROM耦合，在移动前沿和弹性波问题中优于静态分配，实现预测性模型保真度自适应。
AI 中文摘要
混合区域分解方法为耦合全阶模型（FOM）和降阶模型（ROM）提供了灵活的框架，但通常假设每个子域分配的模型在整个模拟过程中是固定的。这对于瞬态问题具有局限性，因为在这些问题中，局部特征会在域中传播，需要高保真分辨率的区域会随时间变化。我们提出了一种基于强化学习（RL）的方法，用于在线自适应FOM-ROM模型耦合，该耦合通过重叠Schwarz交替方法（O-SAM）实现，这是一种迭代区域分解方法，通过重叠界面上的传输边界条件交换解信息，同时求解子域局部问题。深度Q网络（DQNs）被离线训练，以在子域局部FOM和预训练的算子推断（OpInf）ROM之间进行选择，使用平衡精度、成本和模型切换频率的奖励。训练完成后，策略被部署用于预测训练期间未见的问题实例，无需参考FOM解。我们在两个示例上展示了该方法：一个具有移动前沿的一维对流扩散问题，以及一个在this http URL固体力学代码中实现的三维线弹性波传播问题。对于对流扩散基准，学习到的策略在前沿传播时动态分配高保真分辨率，并优于静态FOM/ROM分配；让代理同时调整区域分解没有进一步的好处。对于弹性波基准，针对二域和三域分解学习到的策略通过将FOM分配给包含波的子域，并将ROM分配给其他子域来跟踪传播的波，符合预期。我们的结果证明了RL在Schwarz基混合模拟中实现预测性在线模型保真度自适应的潜力。
英文摘要
Hybrid domain decomposition methods provide a flexible framework for coupling full order models (FOMs) and reduced order models (ROMs), but typically assume the model assigned to each subdomain is fixed throughout a simulation. This is limiting for transient problems in which localized features propagate through the domain and the regions requiring high-fidelity resolution change over time. We introduce a reinforcement learning (RL)-based approach for online adaptation of FOM-ROM models coupled via the overlapping Schwarz alternating method (O-SAM), an iterative domain decomposition method that solves subdomain-local problems while exchanging solution information through transmission boundary conditions on overlapping interfaces. Deep Q-networks (DQNs) are trained offline to select among subdomain-local FOMs and pre-trained Operator Inference (OpInf) ROMs using a reward balancing accuracy, cost, and model-switching frequency. Once trained, the policies are deployed predictively on problem instances not seen during training, without requiring a reference FOM solution. We demonstrate the approach on two examples: a 1D advection-diffusion problem with a moving front, and a 3D linear elastic wave propagation problem implemented in the Norma.jl solid mechanics code. For the advection-diffusion benchmark, the learned policy dynamically allocates high-fidelity resolution as the front propagates and outperforms static FOM/ROM assignments; letting the agent also adapt the domain decomposition provides no further benefit. For the elastic wave benchmark, learned policies for two and three subdomain decompositions track the propagating wave by assigning FOMs to subdomains containing the wave and ROMs elsewhere, as expected. Our results demonstrate the potential of RL to enable predictive online adaptation of model fidelity within Schwarz-based hybrid simulations.
