Dynamic Mode Decomposition and Koopman Theory

Sourya Dey

Publication date: 14 November 2022

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.

Has companion code repository: https://github.com/galoisinc/dlkoopman

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