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

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Codice articolo 18396097819

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

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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.