Chapter 2 - Higher order dynamic mode decomposition

Abstract

This chapter is devoted to the description of the higher order dynamic mode decomposition, which is an improvement of the standard dynamic mode decomposition method. The new method uses, not only each given snapshot, but also a set of d−1 time-lagged snapshots. After establishing the necessity of improving the standard dynamic mode decomposition method, using the concepts of spectral and spatial complexities, the analysis proceeds by describing an algorithm for higher order dynamic mode decomposition, called the DMD-d algorithm. Although, the DMD-1 algorithm is the particular case of DMD-d for d=1, for the sake of clarity, these two cases, d=1 and d>1, are considered separately. The method is illustrated in some toy models.