Latent Modes Of Nonlinear Flows (Elements In Non-Local Data Interactions: Foundations And Applications)

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.

• | Author: Ido Cohen, Guy Gilboa
• | Publisher: Cambridge University Press
• | Publication Date: Jun 29, 2023
• | Number of Pages: 64 pages
• | Language: English
• | Binding: Paperback
• | ISBN-10: 1009323857
• | ISBN-13: 9781009323857