The Multiverse of Dynamic Mode Decomposition Algorithms Article Swipe

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Matthew J. Colbrook ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2312.00137

Dynamic Mode Decomposition (DMD) is a popular data-driven analysis technique used to decompose complex, nonlinear systems into a set of modes, revealing underlying patterns and dynamics through spectral analysis. This review presents a comprehensive and pedagogical examination of DMD, emphasizing the role of Koopman operators in transforming complex nonlinear dynamics into a linear framework. A distinctive feature of this review is its focus on the relationship between DMD and the spectral properties of Koopman operators, with particular emphasis on the theory and practice of DMD algorithms for spectral computations. We explore the diverse "multiverse" of DMD methods, categorized into three main areas: linear regression-based methods, Galerkin approximations, and structure-preserving techniques. Each category is studied for its unique contributions and challenges, providing a detailed overview of significant algorithms and their applications as outlined in Table 1. We include a MATLAB package with examples and applications to enhance the practical understanding of these methods. This review serves as both a practical guide and a theoretical reference for various DMD methods, accessible to both experts and newcomers, and enabling readers to delve into their areas of interest in the expansive field of DMD.

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Computer Science

Algorithm

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Mathematics

Machine Learning

Human–Computer Interaction

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Dynamic mode decomposition Computer science Nonlinear system Field (mathematics) Expansive Algorithm Theoretical computer science Focus (optics) Mode (computer interface) Mathematics Machine learning Human–computer interaction Physics Pure mathematics Optics Quantum mechanics Thermodynamics Compressive strength

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2312.00137
PDF: https://arxiv.org/pdf/2312.00137
OA Status: green
Cited By: 4
Related Works: 10
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OpenAlex ID: https://openalex.org/W4389325422

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DOI: https://doi.org/10.48550/arxiv.2312.00137

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Title: The Multiverse of Dynamic Mode Decomposition Algorithms

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Type: preprint

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Language: en

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Publication year: 2023

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Publication date: 2023-11-30

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Authors: Matthew J. Colbrook

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Landing page: https://arxiv.org/abs/2312.00137

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Concepts: Dynamic mode decomposition, Computer science, Nonlinear system, Field (mathematics), Expansive, Algorithm, Theoretical computer science, Focus (optics), Mode (computer interface), Mathematics, Machine learning, Human–computer interaction, Physics, Pure mathematics, Optics, Quantum mechanics, Thermodynamics, Compressive strength

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Cited by: 4

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Citations by year (recent): 2025: 2, 2024: 1, 2023: 1

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Related works (count): 10

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