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ON DYNAMIC MODE DECOMPOSITION: THEORY AND …

Manuscript submitted to the Journal of Computational DynamicsON DYNAMIC MODE DECOMPOSITION: THEORY AND APPLICATIONSJ onathan H. Tu, Clarence W. Rowley, Dirk M. Luchtenburg,Dept. of Mechanical and Aerospace EngineeringPrinceton UniversityPrinceton, NJ 08544, USAS teven L. Brunton, and J. Nathan KutzDept. of Applied MathematicsUniversity of WashingtonSeattle, WA 98195, introduced in the fluid mechanics community, dynamicmode decomposition (DMD) has emerged as a powerful tool for analyzing thedynamics of nonlinear systems. However, existing DMD THEORY deals primarilywith sequential time series for which the measurement dimension is much largerthan the number of measurements taken. We present a theoretical frameworkin which we define DMD as the eigendecomposition of an approximating lin-ear operator. This generalizes DMD to a larger class of datasets, includingnonsequential time series. We demonstrate the utility of this approach by pre-senting novel sampling strategies that increase computational efficiency andmitigate the effects of noise, respectively.

accepted SVD-based DMD algorithm [8]. A number of examples are presented in Section3. These explore the application of DMD to rank-de cient datasets and nonsequential time series. Section4describes the connections between DMD and Koopman operator theory, the ERA, and LIM, respectively. We summarize our results in Section5. 2. Theory.

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