Buch, Englisch, 75 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 100 g
Reihe: Elements in Non-local Data Interactions: Foundations and Applications
Buch, Englisch, 75 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 100 g
Reihe: Elements in Non-local Data Interactions: Foundations and Applications
ISBN: 978-1-009-32385-7
Verlag: Cambridge University Press
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.
Autoren/Hrsg.
Weitere Infos & Material
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.
