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.

Many of the papers cited above mention the idea that DMD is able to character-ize nonlinear dynamics through an analysis of some approximating linear system. In this work, we build on this notion. We present DMD as an analysis of pairs of n-dimensional data vectors (xk;yk), in contrast to the sequential time series that are typically considered.

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