A Prony Approximation of Koopman Mode Decomposition

Koopman Mode Decomposition (KMD) is an emerging methodology to investigate a nonlinear spatiotemporal evolution via the point spectrum of the so-called Koopman operator defined for arbitrary nonlinear dynamical systems. Prony analysis is widely used in applications and is a methodology to reconstruct a sparse sum of exponentials from finite sampled data. In this paper, we show that a vector version of the Prony analysis provides a finite approximation of the KMD. This leads to an alternative algorithm for computing the Koopman modes and eigenvalues directly from data that is especially suitable to data with small-spatial and large-temporal snapshots. The algorithm is demonstrated by applying it to data on physical power flows sampled from the 2006 system disturbance of the UCTE interconnected grid.