Entropic Regression DMD (ERDMD) Discovers Informative Sparse and Nonuniformly Time Delayed Models
This work addresses the challenge of identifying multiscale features in dynamic systems for researchers in computational physics or data-driven modeling, though it appears incremental as it builds on existing HODMD and entropic regression techniques.
The authors tackled the problem of building high-fidelity time-delay dynamic mode decomposition (DMD) models by developing ERDMD, a method that uses entropic regression to discover optimal nonuniform time delays, resulting in efficient and robust models that produce excellent reconstructions with minimal complexity on chaotic attractor datasets.
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.