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Latent Modes of Nonlinear Flows (Cohen, Ido / Gilboa, Guy)
Latent Modes of Nonlinear Flows
Untertitel A Koopman Theory Analysis
Autor Cohen, Ido / Gilboa, Guy
Verlag Cambridge Academic
Co-Verlag Cambridge University Press (Imprint/Brand)
Sprache Englisch
Einband Kartonierter Einband (Kt)
Erscheinungsjahr 2023
Artikelnummer 44169166
ISBN 978-1-009-32385-7
Reihe Elements in Non-local Data Interactions: Foundations and Applications
CHF 36.75
Lieferbar in ca. 10-20 Arbeitstagen
Zusammenfassung
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).

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.