A concise introduction to Koopman operator theory and the Extended Dynamic Mode Decomposition

TL;DR

This paper offers a clear, concise overview of Koopman operator theory and its relation to Dynamic Mode Decomposition (DMD) and EDMD, emphasizing theoretical and algorithmic connections.

Contribution

It provides a succinct, well-structured exposition that clarifies the relationships between Koopman theory and DMD/EDMD, aiding understanding of the subject.

Findings

Clarifies the connections between Koopman operator theory and DMD/EDMD

Provides consistent notation for better comprehension

Highlights the theoretical and algorithmic relationships

Abstract

The framework of Koopman operator theory is discussed along with its connections to Dynamic Mode Decomposition (DMD) and (Kernel) Extended Dynamic Mode Decomposition (EDMD). This paper provides a succinct overview with consistent notation. The authors hope to provide an exposition that more naturally emphasizes the connections between theory and algorithms which may result in a sense of clarity on the subject.