发表机构
University of Stuttgart; Karlsruhe Institute of Technology; University of California San Diego; University of Wisconsin-Madison（斯图加特大学; 卡尔斯鲁厄理工学院; 加州大学圣地亚哥分校; 威斯康星大学麦迪逊分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文扩展算子推断框架以纳入Petrov-Galerkin投影，保持系统稳定性与无源性，提出强制端口哈密顿结构的凸优化方法，并在多个基准问题上验证有效性。
AI 中文摘要
数据驱动的模型降阶方法（如算子推断）能够直接从高维时域数据中高效构建降阶模型。标准算子推断通常通过在指定的低维子空间中，从投影快照数据中辨识降阶算子，来寻求Galerkin型降阶模型。由此产生的推断问题被表述为一个最小二乘问题，该问题具有高效的闭式解。然而，众所周知，对于线性时不变系统，侵入式模型降阶中的Petrov-Galerkin投影还能额外保持重要的系统性质，如稳定性和无源性。为了克服标准算子推断的局限性，我们将线性时不变系统的框架扩展以纳入Petrov-Galerkin投影，并提供了侵入式与非侵入式降阶算子之间的显式误差表达式和界，从而推广了文献中的结果。我们在耗散系统和端口哈密顿系统的背景下演示了所提出的方法。此外，我们引入了一种新颖的凸优化公式，该公式显式地在推断的算子上强制施加端口哈密顿结构。所提出方法的有效性在几个公认的基准问题上得到了验证，包括CD播放器、大气模型、质量-弹簧-阻尼器系统以及孔隙弹性系统。
英文摘要
Data-driven model order reduction methods such as operator inference enable the efficient construction of reduced-order models directly from high-dimensional time-domain data. Standard operator inference typically seeks a Galerkin-type reduced model in a prescribed low-dimensional subspace by identifying its reduced operators from projected snapshot data. The resulting inference problem is formulated as a least-squares problem admitting an efficient closed-form solution. However, it is well known from intrusive model order reduction for linear time-invariant systems that Petrov-Galerkin projections can additionally preserve important system properties such as stability and passivity. To overcome the limitations of standard operator inference, we extend the framework for linear time-invariant systems to incorporate Petrov-Galerkin projections and provide explicit error expressions and bounds between the intrusive and nonintrusive reduced operators, thus generalizing results from the literature. We demonstrate the proposed approach in the context of dissipative and port-Hamiltonian systems. Furthermore, we introduce a novel convex optimization formulation that explicitly enforces the port-Hamiltonian structure on the inferred operators. The effectiveness of the proposed methods is demonstrated on several well-established benchmark problems, including the CD player, an atmospheric model, a mass-spring-damper system, and a poroelasticity system.
