发表机构
Rice University; National Yang Ming Chiao Tung University; Sandia National Laboratories; Virginia Tech（莱斯大学; 国立阳明交通大学; 桑迪亚国家实验室; 弗吉尼亚理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出在线演化-滤波-松弛（EFR）策略，通过空间滤波提升算子推断降阶模型的长期稳定性，减少正则化需求，并在多个流体问题中将预测误差降低一个数量级。
AI 中文摘要
本文针对复杂流体流动模拟的算子推断（OpInf）降阶模型（ROMs）的长期稳定性，提出了一种在线演化-滤波-松弛（EFR）策略。新EFR-OpInf策略的主要创新在于，在在线（即在学习的ROM在线评估层面）使用受大涡模拟启发的空间滤波，以显著提高标准OpInf的长期稳定性和预测性能。此外，EFR-OpInf策略减少甚至在某些情况下消除了对标准$L^2$正则化的需求，同时为OpInf超参数提供了物理可解释性。EFR-OpInf框架是模块化的，易于集成到现有的OpInf工作流程中，并支持用户选择的ROM滤波策略。我们使用完全非侵入式的基于投影的ROM滤波器、ROM微分滤波器以及混合投影-微分ROM滤波器来展示EFR-OpInf的有效性。新的EFR-OpInf模型在高Péclet数对流-扩散-反应问题（该问题嵌入了一个参数的变化）以及两个非定常Navier-Stokes问题（聚焦于训练时间范围之外的预测）上进行了评估：一个过渡性的二维圆柱绕流和一个三维湍流最小通道流。在这三种场景中，与标准OpInf相比，EFR-OpInf可将预测误差降低多达一个数量级。此外，在标准OpInf发散的情况下，EFR-OpInf在长预测时间范围内保持稳定。根据所使用的ROM滤波器，EFR-OpInf的计算成本与标准OpInf相当。
英文摘要
This paper introduces an online evolve--filter--relax (EFR) strategy for long-term stability of Operator Inference (OpInf) reduced-order models (ROMs) of complex fluid flow simulations. The main novelty of the new EFR-OpInf strategy is the use of online (i.e., at the learned ROM online evaluation level) spatial filtering inspired from large eddy simulation to significantly improve long-term stability and predictive performance of standard OpInf. Furthermore, the EFR-OpInf strategy reduces, and in some cases even eliminates, the need for standard $L^2$ regularization, while providing physical interpretability for the OpInf hyperparameters. The EFR-OpInf framework is modular, readily integrated into existing OpInf workflows, and accommodates a user-selected ROM filtering strategy. We demonstrate the EFR-OpInf's effectiveness using a fully non-intrusive projection-based ROM filter, a ROM differential filter, and a hybrid projection-differential ROM filter. The new EFR-OpInf models are evaluated on a high-Péclet-number convection--diffusion--reaction problem that embeds the variation in one parameter and two unsteady Navier--Stokes problems that focus on predictions beyond a training horizon: a transitional two-dimensional flow past a cylinder and a three-dimensional turbulent minimal channel flow. Across these three scenarios, EFR-OpInf can reduce prediction errors by up to an order of magnitude relative to standard OpInf. Moreover, EFR-OpInf remains stable over long prediction horizons in cases where standard OpInf diverges. Depending on the ROM filter used, EFR-OpInf's computational cost is comparable to that of standard OpInf.
Comments41 pages, 44 figures
