The systematic and physics‐infused construction of a projection‐based reduced‐order model (ROM) shows the capability to replicate the original high‐dimensional system's dynamical evolution but with a fractional computational cost. However, certain nonlinear features and high‐frequency contributions may be lost throughout the aggressive order reduction. Thus, ROMs in a broad category of fluid dynamics applications require stabilization and closure methods to compensate for the key contributions missed through the model order reduction. A new stabilization method for nonlinear ROMs is proposed in this study that learns a linear control law to drive the nonlinear ROM toward maximum agreement with the full‐order model, where a total power constraint guarantees the stability of the nonlinear ROM. This new method achieves both stability and accuracy for nonlinear proper orthogonal decomposition‐Galerkin ROMs in two chosen applications with strong shock‐wake interactions and unsteady oscillations, which trigger strong instabilities in the original ROMs before stabilization. A multistage layout is designed to further enhance the proposed stabilization method for more efficient and robust stabilization of nonlinear ROMs with a large number of unstable modes.

中文翻译：

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非线性降阶模型稳定的全局特征值重新分配方法

基于投影的降阶模型（ROM）的系统化和物理注入构造显示出具有复制原始高维系统动态演化的能力，但计算成本却很小。但是，在整个主动降阶过程中，某些非线性特征和高频贡献可能会丢失。因此，广泛的流体动力学应用中的ROM需要稳定和封闭方法来补偿因模型阶数减少而遗漏的关键作用。本研究提出了一种新的非线性ROM稳定方法，该方法学习一种线性控制律，以驱动非线性ROM与全阶模型达到最大一致，其中总功率约束保证了非线性ROM的稳定性。这种新方法在两个选定的应用中为非线性适当的正交分解加勒金ROM带来了稳定性和准确性，具有强烈的震颤相互作用和非稳态振荡，这会在稳定之前在原始ROM中引发强烈的不稳定性。设计了一个多级布局，以进一步增强所提出的稳定化方法，以便对具有大量不稳定模式的非线性ROM进行更有效和更稳定的稳定化。