Latent Modes of Nonlinear Flows
A Koopman Theory Analysis
Published on 21. June 2023
978-1-009-32386-4 (ISBN)
Description
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.
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Series
Language
English
Place of publication
Cambridge
United Kingdom
Illustrations
Worked examples or Exercises
File size
10,19 MB
ISBN-13
978-1-009-32386-4 (9781009323864)
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Book
06/2023
Cambridge University Press
€24.00
Shipment within 15-20 days
Persons
Content
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.
