Latent Modes of Nonlinear Flows

Latent Modes of Nonlinear Flows
Author :
Publisher : Cambridge University Press
Total Pages : 64
Release :
ISBN-10 : 9781009323864
ISBN-13 : 1009323865
Rating : 4/5 (865 Downloads)

Book Synopsis Latent Modes of Nonlinear Flows by : Ido Cohen

Download or read book Latent Modes of Nonlinear Flows written by Ido Cohen and published by Cambridge University Press. This book was released on 2023-05-31 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


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