IDEAS home Printed from https://ideas.repec.org/a/hin/complx/6920783.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/8503/2018/6920783.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/8503/2018/6920783.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2018/6920783?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mariela González-Narváez & María José Fernández-Gómez & Susana Mendes & José-Luis Molina & Omar Ruiz-Barzola & Purificación Galindo-Villardón, 2021. "Study of Temporal Variations in Species–Environment Association through an Innovative Multivariate Method: MixSTATICO," Sustainability, MDPI, vol. 13(11), pages 1-25, May.
    2. Meyners, Michael & Qannari, El Mostafa, 2001. "Relating principal component analysis on merged data sets to a regression approach," Technical Reports 2001,47, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    3. Yuefeng Han & Rong Chen & Dan Yang & Cun-Hui Zhang, 2020. "Tensor Factor Model Estimation by Iterative Projection," Papers 2006.02611, arXiv.org, revised Jul 2024.
    4. DELL'ANNO, Roberto & VILLA, Stefania, 2012. "Growth in Transition Countries: Big Bang versus Gradualism," CELPE Discussion Papers 122, CELPE - CEnter for Labor and Political Economics, University of Salerno, Italy.
    5. Henk Kiers, 1991. "Hierarchical relations among three-way methods," Psychometrika, Springer;The Psychometric Society, vol. 56(3), pages 449-470, September.
    6. Willem Kloot & Pieter Kroonenberg, 1985. "External analysis with three-mode principal component models," Psychometrika, Springer;The Psychometric Society, vol. 50(4), pages 479-494, December.
    7. Pieter M. Kroonenberg & Cornelis J. Lammers & Ineke Stoop, 1985. "Three-Mode Principal Component Analysis of Multivariate Longitudinal Organizational Data," Sociological Methods & Research, , vol. 14(2), pages 99-136, November.
    8. Elisa Frutos-Bernal & Ángel Martín del Rey & Irene Mariñas-Collado & María Teresa Santos-Martín, 2022. "An Analysis of Travel Patterns in Barcelona Metro Using Tucker3 Decomposition," Mathematics, MDPI, vol. 10(7), pages 1-17, March.
    9. Xinhai Liu & Wolfgang Glänzel & Bart De Moor, 2011. "Hybrid clustering of multi-view data via Tucker-2 model and its application," Scientometrics, Springer;Akadémiai Kiadó, vol. 88(3), pages 819-839, September.
    10. Yoshio Takane & Forrest Young & Jan Leeuw, 1977. "Nonmetric individual differences multidimensional scaling: An alternating least squares method with optimal scaling features," Psychometrika, Springer;The Psychometric Society, vol. 42(1), pages 7-67, March.
    11. Lampartová, Alžběta & Lampart, Marek, 2024. "Exploring diverse trajectory patterns in nonlinear dynamic systems," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    12. Dawn Iacobucci & Doug Grisaffe, 2018. "Perceptual maps via enhanced correspondence analysis: representing confidence regions to clarify brand positions," Journal of Marketing Analytics, Palgrave Macmillan, vol. 6(3), pages 72-83, September.
    13. D'Urso, Pierpaolo & Giordani, Paolo, 2003. "A least squares approach to Principal Component Analysis for interval valued data," Economics & Statistics Discussion Papers esdp03013, University of Molise, Department of Economics.
    14. Serrano Cinca, C. & Mar Molinero, C. & Gallizo Larraz, J.L., 2005. "Country and size effects in financial ratios: A European perspective," Global Finance Journal, Elsevier, vol. 16(1), pages 26-47, August.
    15. Giuseppe Brandi & Ruggero Gramatica & Tiziana Di Matteo, 2019. "Unveil stock correlation via a new tensor-based decomposition method," Papers 1911.06126, arXiv.org, revised Apr 2020.
    16. Rizzi, Alfredo & Vichi, Maurizio, 1995. "Representation, synthesis, variability and data preprocessing of a three-way data set," Computational Statistics & Data Analysis, Elsevier, vol. 19(2), pages 203-222, February.
    17. Dongheon Shin & Kyungnam Ko, 2019. "Application of the Nacelle Transfer Function by a Nacelle-Mounted Light Detection and Ranging System to Wind Turbine Power Performance Measurement," Energies, MDPI, vol. 12(6), pages 1-15, March.
    18. Eric Jondeau & Emmanuel Jurczenko & Michael Rockinger, 2018. "Moment Component Analysis: An Illustration With International Stock Markets," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(4), pages 576-598, October.
    19. Kunz, Werner, 2007. "Visualization of competitive market structure by means of choice data," SFB 649 Discussion Papers 2007-032, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    20. S. Lipovetsky, 2009. "Global Priority Estimation in Multiperson Decision Making," Journal of Optimization Theory and Applications, Springer, vol. 140(1), pages 77-91, January.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hin:complx:6920783. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.