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.
Original language | English |
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Article number | 1809 |
Number of pages | 14 |
Journal | Mathematics |
Volume | 11 |
Issue number | 8 |
Publication status | Published - 11 Apr 2023 |
Keywords
- high order dynamic mode decomposition
- tensor-train decomposition
- dynamical systems
- data driven model
- power systems