Dynamic Mode Decomposition: Theory and Data Reconstruction
Abstract¶
Dynamic Mode Decomposition (DMD) is a data-driven decomposition technique extracting spatio-temporal patterns of time-dependent phenomena. In this paper, we perform a comprehensive theoretical analysis of various variants of DMD. We provide a systematic advancement of these and examine the interrelations. In addition, several results of each variant are proven. Our main result is the exact reconstruction property. To this end, a new modification of scaling factors is presented and a new concept of an error scaling is introduced to guarantee an error-free reconstruction of the data.
Summary¶
Tutorial and survey that presents theoretical analysis of DMD with a focus on data reconstruction from DMD modes, addressing the relationship between DMD approximations and the underlying dynamics of the system.