Ido Cohen, Guy Gilboa

Latent Modes of Nonlinear Flows (eBook, PDF)

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 31. Mai 2023
• Englisch
• ISBN-13: 9781009323864
• Artikelnr.: 68948259

Inhaltsangabe

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.