@article{article_1512698, title={Koopman operator theory and dynamic mode decomposition in data-driven science and engineering: A comprehensive review}, journal={Mathematical Modelling and Numerical Simulation with Applications}, volume={4}, pages={562–594}, year={2024}, DOI={10.53391/mmnsa.1512698}, url={https://izlik.org/JA82EG76UG}, author={Ghosh, Ramen and Mcafee, Marion}, keywords={Applied Koopman operator, data-driven dynamical systems and control, non-linear systems, data-driven estimation and prediction}, abstract={Poincaré’s geometric representation, while historically fundamental in dynamical system analysis, faces challenges with high-dimensional and uncertain systems in modern engineering and data analysis. This article extensively explores Koopman Operator Theory (KOT) and Dynamic Mode Decomposition (DMD) within data-driven science and engineering and advocates for a conceptual shift toward observable dynamics, emphasizing KOT’s capacity to capture nonlinear dynamics in infinite-dimensional space. The potential practical applications of Koopman-based methods are highlighted. Leveraging Poincaré’s framework, the limitations of traditional methods are discussed. The review also addresses the growing significance of data-driven methodologies for modelling, predicting, and controlling complex systems.}, number={4}