发表机构
MACS, CNAM; Laboratory of Biomechanics and Bioengineering, Université de Technologie de Compiègne, CNRS（法国国立工艺学院; 康普依涅理工大学生物力学与生物工程实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出在线自适应非侵入式降阶建模策略，基于Grassmann流形插值与子空间更新，预测流固耦合界面力以加速非线性迭代收敛，无需存储高维数据，显著提升精度与效率。
AI 中文摘要
我们提出了一种新颖的在线自适应非侵入式降阶建模策略，用于参数化动力系统，该系统涉及参数依赖和时间依赖的降阶基。所提出的框架基于统一的Grassmann流形公式，结合了三个关键组成部分：针对未见参数的局部降阶子空间插值、由传入的高保真快照驱动的测地线在线子空间更新，以及依赖于Grassmann距离加权和Procrustes对齐的潜空间回归策略，以一致地聚合来自多个局部模型的预测。该自适应降阶模型嵌入到分区流固耦合框架中，用于预测流体界面力，为非线性耦合迭代提供准确的初始猜测，从而在保证精度的同时实现计算加速。降阶基和回归算子均在模拟过程中独立自适应，且无需存储高维流式数据，在保持计算效率的同时显著提高了预测能力。在参考流固耦合测试案例上的数值结果表明，与静态和全局降阶模型相比，所提出的模型具有更高的精度，并显著减少了收敛所需的定点迭代次数。该框架为高效模拟非线性参数依赖的多物理场问题提供了一种灵活且完全非侵入式的方法。
英文摘要
We introduce a novel online adaptive non-intrusive reduced-order modeling strategy for parameterized dynamical systems involving parameter and time-dependent reduced bases. The proposed framework is based on a unified Grassmann manifold formulation combining three key components: interpolation of local reduced subspaces for unseen parameters, geodesic online subspace updates driven by incoming high-fidelity snapshots, and a latent-space regression strategy relying on Grassmann-distance weighting and Procrustes alignment to consistently aggregate predictions from multiple local models. The adaptive reduced-order model is embedded in a partitioned fluid-structure interaction framework, where it predicts fluid interface forces to provide accurate initial guesses for the nonlinear coupling iterations, thus achieving computational speedups with no loss of accuracy. The reduced basis and the regression operators are adapted independently during the simulation and without requiring the storage of high-dimensional streaming data, preserving computational efficiency while substantially improving predictive capabilities. Numerical results on reference FSI test cases demonstrate superior accuracy with respect to static and global reduced-order models, leading to a significant reduction in the number of fixed-point iterations required for convergence. The proposed framework offers a flexible and fully non-intrusive approach for the efficient simulation of nonlinear parameter-dependent multiphysics problems.
