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  3. Latent Modes of Nonlinear Flows
  • Cited by 3
  • Ido Cohen, Technion - Israel Institute of Technology, Guy Gilboa, Technion - Israel Institute of Technology
Publisher:
Cambridge University Press
Online publication date:
May 2023
Print publication year:
2023
Online ISBN:
9781009323826
DOI:
https://doi.org/10.1017/9781009323826
Subjects:
Mathematics, Computational Science
Series:
Elements in Non-local Data Interactions: Foundations and Applications
Information

Book description

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.

References

References

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