Tensor train based higher order Dynamic Mode Decomposition for dynamical systems

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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 low-rank tensor decomposition of potentially high-dimensional data sets. 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. 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 provide 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 languageEnglish
Publication statusAccepted/In press - 7 Apr 2023


  • high order dynamic mode decomposition
  • tensor-train decomposition
  • dynamical systems
  • data driven model
  • power systems


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