Koopman operator theory and dynamic mode decomposition in data-driven science and engineering: A comprehensive review

Year 2024, Volume: 4 Issue: 4, 562 - 594, 30.12.2024

Ramen Ghosh , Marion Mcafee

https://doi.org/10.53391/mmnsa.1512698

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.

Keywords

Applied Koopman operator, data-driven dynamical systems and control, non-linear systems, data-driven estimation and prediction

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