Latent Modes of Nonlinear Flows: A Koopman Theory Analysis

Ido Cohen

ISBN 10: 1009323857 / ISBN 13: 9781009323857

Edité par Cambridge University Press 2023-04-01, 2023

A propos de cet article

N° de réf. du vendeur 6666-GRD-9781009323857

Détails bibliographiques

• Titre: Latent Modes of Nonlinear Flows: A Koopman Theory Analysis
• Éditeur: Cambridge University Press 2023-04-01
• Date de parution: 2023
• Langue: anglais
• ISBN à 10 chiffres: 1009323857
• ISBN à 13 chiffres: 9781009323857
• Reliure: Paperback
• État de l'article: New

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Synopsis

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.