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Analyzing Nonlinear Dynamics via Data-Driven Dynamic Mode Decomposition-Like Methods

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  • Soledad Le Clainche
  • José M. Vega

Abstract

This article presents a review on two methods based on dynamic mode decomposition and its multiple applications, focusing on higher order dynamic mode decomposition (which provides a purely temporal Fourier-like decomposition) and spatiotemporal Koopman decomposition (which gives a spatiotemporal Fourier-like decomposition). These methods are purely data-driven, using either numerical or experimental data, and permit reconstructing the given data and identifying the temporal growth rates and frequencies involved in the dynamics and the spatial growth rates and wavenumbers in the case of the spatiotemporal Koopman decomposition. Thus, they may be used to either identify and extrapolate the dynamics from transient behavior to permanent dynamics or construct efficient, purely data-driven reduced order models.

Suggested Citation

  • Soledad Le Clainche & José M. Vega, 2018. "Analyzing Nonlinear Dynamics via Data-Driven Dynamic Mode Decomposition-Like Methods," Complexity, Hindawi, vol. 2018, pages 1-21, December.
    • Handle: RePEc:hin:complx:6920783
    DOI: 10.1155/2018/6920783
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    References listed on IDEAS

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    1. Ledyard Tucker, 1966. "Some mathematical notes on three-mode factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 31(3), pages 279-311, September.
    2. Steven L. Brunton & Bingni W. Brunton & Joshua L. Proctor & Eurika Kaiser & J. Nathan Kutz, 2017. "Chaos as an intermittently forced linear system," Nature Communications, Nature, vol. 8(1), pages 1-9, December.
    3. Soledad Le Clainche & Luis S. Lorente & José M. Vega, 2018. "Wind Predictions Upstream Wind Turbines from a LiDAR Database," Energies, MDPI, vol. 11(3), pages 1-15, March.
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