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

Ramen Ghosh; Marion Mcafee

doi:10.53391/mmnsa.1512698

EN

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

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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Details

Primary Language

English

Subjects

Dynamical Systems in Applications

Journal Section

Review Article

Authors

Ramen Ghosh ^*
0000-0003-0446-3101
Ireland

Marion Mcafee
0000-0002-1434-1215
Ireland

Publication Date

December 30, 2024

Submission Date

July 8, 2024

Acceptance Date

December 27, 2024

Published in Issue

Year 2024 Volume: 4 Number: 4

DOI

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

IZ

https://izlik.org/JA82EG76UG

APA

Ghosh, R., & Mcafee, M. (2024). Koopman operator theory and dynamic mode decomposition in data-driven science and engineering: A comprehensive review. Mathematical Modelling and Numerical Simulation With Applications, 4(4), 562-594. https://doi.org/10.53391/mmnsa.1512698

AMA

1.Ghosh R, Mcafee M. Koopman operator theory and dynamic mode decomposition in data-driven science and engineering: A comprehensive review. MMNSA. 2024;4(4):562-594. doi:10.53391/mmnsa.1512698

Chicago

Ghosh, Ramen, and Marion Mcafee. 2024. “Koopman Operator Theory and Dynamic Mode Decomposition in Data-Driven Science and Engineering: A Comprehensive Review”. Mathematical Modelling and Numerical Simulation With Applications 4 (4): 562-94. https://doi.org/10.53391/mmnsa.1512698.

EndNote

Ghosh R, Mcafee M (December 1, 2024) Koopman operator theory and dynamic mode decomposition in data-driven science and engineering: A comprehensive review. Mathematical Modelling and Numerical Simulation with Applications 4 4 562–594.

IEEE

[1]R. Ghosh and M. Mcafee, “Koopman operator theory and dynamic mode decomposition in data-driven science and engineering: A comprehensive review”, MMNSA, vol. 4, no. 4, pp. 562–594, Dec. 2024, doi: 10.53391/mmnsa.1512698.

ISNAD

Ghosh, Ramen - Mcafee, Marion. “Koopman Operator Theory and Dynamic Mode Decomposition in Data-Driven Science and Engineering: A Comprehensive Review”. Mathematical Modelling and Numerical Simulation with Applications 4/4 (December 1, 2024): 562-594. https://doi.org/10.53391/mmnsa.1512698.

JAMA

1.Ghosh R, Mcafee M. Koopman operator theory and dynamic mode decomposition in data-driven science and engineering: A comprehensive review. MMNSA. 2024;4:562–594.

MLA

Ghosh, Ramen, and Marion Mcafee. “Koopman Operator Theory and Dynamic Mode Decomposition in Data-Driven Science and Engineering: A Comprehensive Review”. Mathematical Modelling and Numerical Simulation With Applications, vol. 4, no. 4, Dec. 2024, pp. 562-94, doi:10.53391/mmnsa.1512698.

Vancouver

1.Ramen Ghosh, Marion Mcafee. Koopman operator theory and dynamic mode decomposition in data-driven science and engineering: A comprehensive review. MMNSA. 2024 Dec. 1;4(4):562-94. doi:10.53391/mmnsa.1512698