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

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 h...

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Bibliographic Details
Published inMathematics (Basel) Vol. 11; no. 8; p. 1809
Main Authors Li, Keren, Utyuzhnikov, Sergey
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.04.2023
Subjects
Algorithms
Approximation
Complexity
Computing time
data-driven model
Decomposition
Decomposition (Mathematics)
dynamic systems
Dynamical systems
Eigenvalues
Eigenvectors
higher-order dynamic mode decomposition
Mathematical analysis
Mathematical research
Mathematics
power systems
System effectiveness
tensor-train decomposition
Tensors
United States
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11081809