A DATA–DRIVEN APPROXIMATION OF THE KOOPMAN OPERATOR: EXTENDING DYNAMIC MODE DECOMPOSITION

Abstract. The Koopman operator is a linear but infinite dimensional opera-tor that governs the evolution of scalar observables defined on the state space of an autonomous dynamical system, and is a powerful tool for the analysis and decomposition of nonlinear dynamical systems. In this manuscript, we present a data driven method for approximating the leading eigenvalues, eigenfunc-tions, and modes of the Koopman operator. The method requires a data set of snapshot pairs and a dictionary of scalar observables, but does not require ex-plicit governing equations or interaction with a “black box ” integrator. We will show that this approach is, in effect, an extension of Dynamic Mode Decompo-sition (DMD), which…