SIAM DS21: Gowtham San Seenivasaharagavan - Mean Subtraction and Mode Selection in DMD скачать в хорошем качестве

SIAM DS21: Gowtham San Seenivasaharagavan - Mean Subtraction and Mode Selection in DMD

Abstract: Koopman mode analysis has rationalized nonlinear phenomena across a plethora of fields. Its numerical implementation via Dynamic Mode Decomposition (DMD) has been extensively deployed and improved upon over the decade. We address the problems of mean subtraction and mode selection in the context of finite dimensional Koopman invariant subspaces. Subtracting the temporal mean of a time series has been a point of contention in Companion matrix DMD. This stems from the potential of said pre-processing to render DMD equivalent to temporal DFT. We prove that this equivalence is impossible when the model order exceeds the dimension of the system. Moreover, its presence is always indicative of an inadequecy of data. We then show that spurious Ritz values can have a one-one correspondence with Ritz vectors of vanishing norm. This observation is seen to extend for mean subtracted data with additional pre-processing. In particular, preserving a Ritz value at 1 or taking a single delay is sufficient for the extension. Authors Gowtham S Seenivasaharagavan, University of California, Santa Barbara, U.S., gowthamsan@ucsb.edu Milan Korda, LAAS-CNRS, Toulouse, France, korda@laas.fr Hassan Arbabi, Massachusetts Institute of Technology, U.S., arbabi@mit.edu Igor Mezic, University of California, Santa Barbara, U.S., mezic@ucsb.edu