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Tensor Train-Based Higher-Order Dynamic Mode Decomposition for Dynamical Systems

Author

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  • Keren Li

    (School of Engineering, University of Manchester, Manchester M13 9PL, UK
    These authors contributed equally to this work.)

  • Sergey Utyuzhnikov

    (School of Engineering, University of Manchester, Manchester M13 9PL, UK
    These authors contributed equally to this work.)

Abstract

Higher-order dynamic mode decomposition (HODMD) has proved to be an efficient tool for the analysis and prediction of complex dynamical systems described by data-driven models. In the present paper, we propose a realization of HODMD that is based on the low-rank tensor decomposition of potentially high-dimensional datasets. It is used to compute the HODMD modes and eigenvalues to effectively reduce the computational complexity of the problem. The proposed extension also provides a more efficient realization of the ordinary dynamic mode decomposition with the use of the tensor-train decomposition. The high efficiency of the tensor-train-based HODMD (TT-HODMD) is illustrated by a few examples, including forecasting the load of a power system, which provides comparisons between TT-HODMD and HODMD with respect to the computing time and accuracy. The developed algorithm can be effectively used for the prediction of high-dimensional dynamical systems.

Suggested Citation

  • Keren Li & Sergey Utyuzhnikov, 2023. "Tensor Train-Based Higher-Order Dynamic Mode Decomposition for Dynamical Systems," Mathematics, MDPI, vol. 11(8), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1809-:d:1120510
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    References listed on IDEAS

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    1. Yang, Jing-Hua & Zhao, Xi-Le & Ji, Teng-Yu & Ma, Tian-Hui & Huang, Ting-Zhu, 2020. "Low-rank tensor train for tensor robust principal component analysis," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    2. Hong, Tao & Pinson, Pierre & Fan, Shu, 2014. "Global Energy Forecasting Competition 2012," International Journal of Forecasting, Elsevier, vol. 30(2), pages 357-363.
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