Dynamic Mode Decomposition—A Numerical Linear Algebra Perspective

Abstract

Data-driven scenarios in analysis and modeling of complex dynamical systems pose formidable challenges to computational science and motivate development of new numerical methods with ever increasing level of sophistication and complexity. An excellent example is computational fluid dynamics (CFD), where the dynamic mode decomposition (DMD) and its enhancement, the sparsity promoting DMD (DMDSP) have emerged as tools of trade for analysis of flow field data, with a host of applications. The problems of high dimension, noisy data, theoretical foundation in connection with the Koopman operator and ergodic theory, and potential applicability in broad spectrum of engineering problems have triggered extensive research and resulted in many theoretical and computational advancements of the DMD framework. This chapter revisits the DMD from the core numerical linear algebra perspective. Recent results on improving numerical robustness and functionality of DMD are reviewed and supplemented with new insights. Further, a new variation of the algorithm is proposed and used as a case study for development of a numerical algorithm in the DMD framework.