Latent Modes of Nonlinear Flows (eBook)

A Koopman Theory Analysis

Ido Cohen, Guy Gilboa (Autoren)

eBook Download: PDF

2023
Cambridge University Press (Verlag)
978-1-009-32386-4 (ISBN)

Infos

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.

Produkt-Details

• Erscheint lt. Verlag: 29.6.2023
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Technik ► Nachrichtentechnik
• ISBN-10: 1-009-32386-5 / 1009323865
• ISBN-13: 978-1-009-32386-4 / 9781009323864