Latent Modes of Nonlinear Flows: A Koopman Theory Analysis (Elements in Non-local Data Interactions: Foundations and Applications)

Cohen, Ido

ISBN 10: 1009323857 / ISBN 13: 9781009323857

Editore: Cambridge University Press, 2023

Riguardo questo articolo

1st edition NO-PA16APR2015-KAP.

Codice articolo 26396097809

Dati bibliografici

• Titolo: Latent Modes of Nonlinear Flows: A Koopman Theory Analysis (Elements in Non-local Data Interactions: Foundations and Applications)
• Editore: Cambridge University Press
• Data di pubblicazione: 2023
• Lingua: Inglese
• ISBN 10: 1009323857
• ISBN 13: 9781009323857
• Rilegatura: Brossura
• Condizione: New

Descrizione articolo

Riassunto

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.