Latent Modes of Nonlinear Flows: A Koopman Theory Analysis

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Ido Cohen (Technion - Israel Institute of Technology) Guy Gilboa (Technion - Israel Institute of Technology)

Latent Modes of Nonlinear Flows

A Koopman Theory Analysis

Ido Cohen (Technion - Israel Institute of Technology), Guy Gilboa (Technion - Israel Institute of Technology)

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English

Cambridge University Press
29 June 2023

Non-linear science; Communications engineering & telecommunications; Signal processing

Series: Elements in Non-local Data Interactions: Foundations and Applications

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.

By: Ido Cohen (Technion - Israel Institute of Technology), Guy Gilboa (Technion - Israel Institute of Technology)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 229mm, Width: 152mm, Spine: 3mm
Weight: 108g
ISBN: 9781009323857
ISBN 10: 1009323857
Series: Elements in Non-local Data Interactions: Foundations and Applications
Pages: 75
Publication Date: 29 June 2023
Audience: General/trade , ELT Advanced
Format: Paperback
Publisher's Status: Active

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.