Entropic Regression DMD (ERDMD) Discovers Informative Sparse and Nonuniformly Time Delayed Models

TL;DR

This paper introduces ERDMD, a novel method that uses entropic regression to discover optimal, sparse, and nonuniform time-delayed DMD models, improving model fidelity and multiscale feature detection in complex systems.

Contribution

The paper develops ERDMD, a new approach combining entropic regression with multi-step DMD to produce efficient, robust, and informative models with nonuniform time delays.

Findings

High fidelity reconstructions on chaotic data sets

Effective identification of multiscale features

Models require minimal complexity for accurate results

Abstract

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.