Latent Modes of Nonlinear Flows
A Koopman Theory Analysis
Seiten
2023
Cambridge University Press (Verlag)
978-1-009-32385-7 (ISBN)
Cambridge University Press (Verlag)
978-1-009-32385-7 (ISBN)
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.
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.
| Erscheinungsdatum | 21.06.2023 |
|---|---|
| Reihe/Serie | Elements in Non-local Data Interactions: Foundations and Applications |
| Zusatzinfo | Worked examples or Exercises |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 153 x 230 mm |
| Gewicht | 132 g |
| Themenwelt | Mathematik / Informatik ► Informatik |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Technik ► Nachrichtentechnik | |
| ISBN-10 | 1-009-32385-7 / 1009323857 |
| ISBN-13 | 978-1-009-32385-7 / 9781009323857 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
| Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
Buch | Softcover (2025)
Springer Vieweg (Verlag)
CHF 62,95
Buch | Softcover (2025)
Springer Fachmedien Wiesbaden (Verlag)
CHF 69,95
Buch | Softcover (2024)
Springer Vieweg (Verlag)
CHF 53,15
