Dynamic Mode Decomposition and Its Application in Various Domains: An Overview

The unprecedented availability of high-fidelity data measurements in various disciplines of engineering and physical and medical sciences reinforces the development of more sophisticated algorithms for data processing and analysis. More advanced algorithms are required to extract the spatiotemporal features concealed in the data that represent the system dynamics. Usage of advanced data-driven algorithms paves the way to understand the associated dominant dynamical behavior and, thus, improves the capacity for various tasks, such as forecasting, control, and modal analysis. One such emerging method for data-driven analysis is dynamic mode decomposition (DMD). The algorithm for DMD is introduced by Peter J. Schmid in 2010 based on the foundation of Koopman operator (Schmid. J Fluid Mech 656:5–28, 2010). It is basically a decomposition algorithm with intelligence to identify the spatial patterns and temporal features of the data measurements. DMD has recently gained improved interest due to its dominant ability to mine meaningful information from available measurements. It has revolutionized the analysis and modeling of physical systems like fluid dynamics, neuroscience, financial trading markets, multimedia, smart grid, etc. The ability to recognize the spatiotemporal patterns makes DMD as prominent among other similar algorithms. DMD algorithm merges the characteristics of proper orthogonal decomposition (POD) and Fourier transform.