Latent Modes of Nonlinear Flows

Ido Cohen

ISBN 10: 1009323857 / ISBN 13: 9781009323857

Editore: Cambridge University Press Jun 2023, 2023

Riguardo questo articolo

Neuware - 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.

Codice articolo 9781009323857

Dati bibliografici

• Titolo: Latent Modes of Nonlinear Flows
• Editore: Cambridge University Press Jun 2023
• Data di pubblicazione: 2023
• Lingua: Inglese
• ISBN 10: 1009323857
• ISBN 13: 9781009323857
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 229 L x 152 A x 3 P (millimetri) 229 millimetri di larghezza per 152 millimetri di altezza per 3 millimetri di profondità
• Peso: 100 grammi

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.