State-Of-The-Art Algorithms For Low-Rank Dynamic Mode Decomposition

TL;DR

This paper reviews advanced algorithms for low-rank dynamic mode decomposition, a technique for approximating high-dimensional dynamical systems, providing detailed insights into current state-of-the-art methods.

Contribution

It offers an in-depth review and additional details on the latest algorithms for low-rank DMD, enhancing understanding of current methodologies.

Findings

Comprehensive overview of state-of-the-art low-rank DMD algorithms

Detailed comparison of different approaches in the literature

Clarification of the mathematical foundations of low-rank DMD

Abstract

This technical note reviews sate-of-the-art algorithms for linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). While repeating several parts of our article "low-rank dynamic mode decomposition: an exact and tractable solution", this work provides additional details useful for building a comprehensive picture of state-of-the-art methods.