Clarifying the effect of mean subtraction on Dynamic Mode Decomposition

Autor:	Seenivasaharagavan, Gowtham S, Korda, Milan, Arbabi, Hassan, Mezić, Igor
Rok vydání:	2021
Předmět:	Mathematics - Dynamical Systems Electrical Engineering and Systems Science - Signal Processing Physics - Data Analysis Statistics and Probability 37M10 37N10 47N20
Druh dokumentu:	Working Paper
Popis:	Any autonomous nonlinear dynamical system can be viewed as a superposition of infinitely many linear processes, through the so-called Koopman mode decomposition. Its data-driven approximation- Dynamic Mode Decomposition (DMD)- has been extensively developed and deployed across a plethora of fields. In this work, we study the effect of subtracting the temporal mean on the DMD approximation, for observables possessing only a finite number of Koopman modes. Pre-processing time-sequential training data by removing the temporal mean has been a point of contention in the Companion matrix formulation of DMD. This stems from the potential of said pre-processing to render DMD equivalent to a temporal Discrete Fourier Transform (DFT). We prove that this equivalence is impossible when the training data is linearly consistent and the order of the DMD approximation exceeds the number of Koopman modes. Since model order and training set size are synonymous in this variant of DMD, the parity of DMD and DFT can, therefore, be indicative of inadequate training data. Comment: 39 pages, 7 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2105.03607 Zobrazit plný text záznamu View this record from Arxiv