Data-driven dynamical systems is a burgeoning field—it connects how measurements of nonlinear dynamical systems and/or complex systems can be used with well-established methods in dynamical systems theory. This is a critically important new direction because the governing equations of many problems under consideration by practitioners in various scientific fields are not typically known. Thus, using data alone to help derive, in an optimal sense, the best dynamical system representation of a given application allows for important new insights. The recently developed dynamic mode decomposition (DMD) is an innovative tool for integrating data with dynamical systems theory. The DMD has deep connections with traditional dynamical systems theory and many recent innovations in compressed sensing and machine learning.
Author(s): J. Nathan Kutz, Steven L. Brunton, Bingni W. Brunton, Joshua L. Proctor
Publisher: SIAM-Society for Industrial and Applied Mathematics
Year: 2016
Language: English
Pages: 241
Tags: Applied Mathematics, Complex Systems, Koopman Theory
Front Matter......Page 1
Chapter 1：Dynamic Mode Decomposition：An Introduction......Page 14
Chapter 2：Fluid Dynamics......Page 38
Chapter 3：Koopman Analysis......Page 52
Chapter 4：Video Processing......Page 67
Chapter 5：Multiresolution Dynamic Mode Decomposition......Page 83
Chapter 6：DMD with Control......Page 102
Chapter 7：Delay Coordinates, ERA, and Hidden Markov Models......Page 115
Chapter 8：Noise and Power......Page 129
Chapter 9：Sparsity and DMD......Page 143
Chapter 10：DMD on Nonlinear Observables......Page 168
Chapter 11：Epidemiology......Page 186
Chapter 12：Neuroscience......Page 194
Chapter 13：Financial Trading......Page 203
Back Matter......Page 215
