Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation time. Optimization techniques are studied to improve either or both of these objectives and decrease the total computational cost of the problem. This paper focuses on the dynamic mode decomposition (DMD) applied to nonlinear PDEs with periodic boundary conditions. It provides a study of a newly proposed optimization framework for the DMD method called the Split DMD.

翻译：长期以来，降阶模型一直被用于理解非线性偏微分方程的行为。自然地，降阶建模技术以牺牲计算精度为代价来缩短计算时间。人们研究了优化技术，旨在改善其中一个或两个目标，并降低问题的总计算成本。本文聚焦于应用于具有周期性边界条件的非线性偏微分方程的动态模态分解。它提供了一种名为分裂动态模态分解的新提出的DMD优化框架的研究。