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

Keren Li and Sergey Utyuzhnikov ()
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Keren Li: School of Engineering, University of Manchester, Manchester M13 9PL, UK
Sergey Utyuzhnikov: School of Engineering, University of Manchester, Manchester M13 9PL, UK

Mathematics, 2023, vol. 11, issue 8, 1-14

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.

Keywords: higher-order dynamic mode decomposition; tensor-train decomposition; dynamic systems; data-driven model; power systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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