A Data–Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition

• Published in: Journal of nonlinear science Vol. 25; no. 6; pp. 1307 - 1346
• Main Authors: Williams, Matthew O., Kevrekidis, Ioannis G., Rowley, Clarence W.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.12.2015
• Subjects: Analysis; Classical Mechanics; Economic Theory/Quantitative Economics/Mathematical Methods; Mathematical and Computational Engineering; Mathematical and Computational Physics; Mathematics; Mathematics and Statistics; Theoretical; Koopman spectral analysis; 37M25; Secondary: 47B33; Data mining; Reduced order models; Set oriented methods; Spectral methods; Primary: 65P99

The Koopman operator is a linear but infinite-dimensional operator that governs the evolution of scalar observables defined on the state space of an autonomous dynamical system and is a powerful tool for the analysis and decomposition of nonlinear dynamical systems. In this manuscript, we present a...