Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems

Description

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. 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