In this work, we present a method which determines optimal multi-step dynamic mode decomposition (DMD) models via entropic regression, which is a nonlinear information flow detection algorithm. Motivated by the higher-order DMD (HODMD) method of \cite{clainche}, and the entropic regression (ER) technique for network detection and model construction found in \cite{bollt, bollt2}, we develop a method that we call ERDMD that produces high fidelity time-delay DMD models that allow for nonuniform time space, and the time spacing is discovered by consider most informativity based on ER. These models are shown to be highly efficient and robust. We test our method over several data sets generated by chaotic attractors and show that we are able to build excellent reconstructions using relatively minimal models. We likewise are able to better identify multiscale features via our models which enhances the utility of dynamic mode decomposition.

翻译：本文提出一种方法，通过熵回归（一种非线性信息流检测算法）确定最优多步动态模态分解模型。受\cite{clainche}提出的高阶动态模态分解方法，以及\cite{bollt, bollt2}中用于网络检测与模型构建的熵回归技术启发，我们开发了一种称为ERDMD的方法，该方法能够生成高保真度的时滞动态模态分解模型。该模型支持非均匀时间间隔，且时间间隔的确定基于熵回归的最大信息量准则。实验表明这些模型具有高效性与鲁棒性。我们在多个混沌吸引子生成的数据集上测试了该方法，证明能够使用相对精简的模型实现优异的系统重构。同时，通过该模型我们能够更好地识别多尺度特征，从而增强了动态模态分解的实用性。