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Series:   Elements in Non-local Data Interactions: Foundations and Applications

Latent Modes of Nonlinear Flows

A Koopman Theory Analysis

Published online by Cambridge University Press:  31 May 2023

Ido Cohen  and
Guy Gilboa
Ido Cohen
Affiliation:
Technion - Israel Institute of Technology
Guy Gilboa
Affiliation:
Technion - Israel Institute of Technology

Summary

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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Keywords

nonlinear decompositiondynamic mode decompositionhomogeneous operatorsgradient flowsnonlinear spectral theoryKoopman eigenfunctionsKoopman mode decomposition
Type
Element
Information
Series: Elements in Non-local Data Interactions: Foundations and Applications
Online ISBN: 9781009323826
Publisher: Cambridge University Press
Print publication: 29 June 2023

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Latent Modes of Nonlinear Flows
  • Ido Cohen, Technion - Israel Institute of Technology, Guy Gilboa, Technion - Israel Institute of Technology
  • Online ISBN: 9781009323826
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Latent Modes of Nonlinear Flows
  • Ido Cohen, Technion - Israel Institute of Technology, Guy Gilboa, Technion - Israel Institute of Technology
  • Online ISBN: 9781009323826
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Latent Modes of Nonlinear Flows
  • Ido Cohen, Technion - Israel Institute of Technology, Guy Gilboa, Technion - Israel Institute of Technology
  • Online ISBN: 9781009323826
Available formats
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