Latent Modes of Nonlinear Flows: A Koopman Theory Analysis (Elements in Non-local Data Interactions: Foundations and Applications)
By
Ido Cohen (Author) Guy Gilboa (Author)
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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. Worked examples or Exercises
More Details
- Contributor: Ido Cohen
- Imprint: Cambridge University Press
- ISBN13: 9781009323857
- Number of Pages: 75
- Packaged Dimensions: 152x229x3mm
- Packaged Weight: 108
- Format: Paperback
- Publisher: Cambridge University Press
- Release Date: 2023-06-29
- Series: Elements in Non-local Data Interactions: Foundations and Applications
- Binding: Paperback / softback
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