Dynamic Mode Decomposition and Koopman Theory

TL;DR

This paper provides a clear, mathematically detailed overview of Dynamic Mode Decomposition and Koopman theory, aiming to facilitate understanding and implementation of these techniques for analyzing non-linear dynamical systems.

Contribution

It offers a comprehensive, step-by-step mathematical explanation of DMD and Koopman theory, including derivations and implementation guidance.

Findings

Enhanced understanding of DMD and Koopman theory

Step-by-step derivations for implementation

Facilitates coding and application of these methods

Abstract

Dynamic Mode Decomposition (DMD) is a technique to approximate generally non-linear dynamical systems using linear techniques, which are better understood and easier to analyze. Koopman theory extends DMD by transforming the original system into a new domain which facilitates linearization. This is a technical report on DMD and Koopman theory, with primary focus on explaining the underlying mathematics in clear and concise form. We include dimensions of vectors and marices, and step-by-step derivations of equations in order to assist the user in easily comprehending these concepts. This report will also enable users to implement DMD and Koopman theory in code.