In this manuscript, we propose a novel reduction framework for obtaining Reduced Order Models (ROMs) of large-scale, nonlinear dynamical systems. We advocate the use of Nonlinear Moment Matching (NLMM) with the Dynamic Mode Decomposition (DMD) to get a much efficient dimensionality reduction scheme. While NLMM does not require the expensive computation of the time-displaced snapshot ensemble of the Full Order Model (FOM) in the offline stage, DMD avoids the evaluation of the nonlinear term in the online stage. Thus, significant savings in terms of the overall CPU-time is achieved. To substantiate our observations, we test the proposed scheme on a variety of benchmark models and compare the results with POD–DEIM for reference.

在此手稿中，我们提出了一种新颖的归约框架，用于获取大型非线性动力学系统的降序模型（ROM）。我们提倡将非线性矩匹配（NLMM）与动态模式分解（DMD）结合使用，以获得高效的降维方案。尽管NLMM不需要在脱机阶段进行全订单模型（FOM）的时移快照整体的昂贵计算，但DMD避免了在在线阶段对非线性项进行评估。因此，就整体CPU时间而言，可实现显着的节省。为了证实我们的观察，我们在各种基准模型上测试了所提出的方案，并将结果与​​POD-DEIM进行比较以供参考。