Latent Modes of Nonlinear Flows - A Koopman Theory Analysis

Extracting the latent underlying structures of complex nonlinear local and nonlocal flows is essential for their analysis and modeling. In this Element the authors attempt to provide a consistent framework through Koopman theory and its related popular discrete approximation - dynamic mode decomposition (DMD). They investigate the conditions to perform appropriate linearization, dimensionality reduction and representation of flows in a highly general setting. The essential elements of this framework are Koopman eigenfunctions (KEFs) for which existence conditions are formulated. This is done by viewing the dynamic as a curve in state-space. These conditions lay the foundations for system reconstruction, global controllability, and observability for nonlinear dynamics. They examine the limitations of DMD through the analysis of Koopman theory and propose a new mode decomposition technique based on the typical time profile of the dynamics.

List of contents

1. Introduction; 2. Preliminaries; 3. Motivation for This Work; 4. Koopman Eigenfunctions and Modes; 5. Koopman Theory for Partial Differential Equation; 6. Mode Decomposition Based on Time State-Space Mapping; 7. Examples; 8. Conclusion; List of Symbols; List of Abbreviations; Appendix A Extended Dynamic Mode Decomposition Induced from Inverse Mapping; Appendix B Sparse Representation; References.

Product details

• Authors: Ido Cohen, Ido (Technion - Israel Institute of Technol Cohen, Ido (Technion - Israel Institute of Technology) Cohen, Guy Gilboa, Guy (Technion - Israel Institute of Technology) Gilboa
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Paperback / Softback
• Released: 01.05.2023
• EAN: 9781009323857
• ISBN: 978-1-0-0932385-7
• No. of pages: 75
• Series: Elements in Non-local Data Interactions: Foundations and Applications; Elements in Non-Local Data Int
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; TECHNOLOGY & ENGINEERING / Signals & Signal Processing, MATHEMATICS / Linear & Nonlinear Programming, Signal Processing, Nonlinear science, Communications engineering / telecommunications