Tensor-based dynamic mode decomposition

Stefan Klus*, Patrick Gelß, Sebastian Peitz, Christof Schütte

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

43 Citations (Scopus)

Abstract

Dynamic mode decomposition (DMD) is a recently developed tool for the analysis of the behavior of complex dynamical systems. In this paper, we will propose an extension of DMD that exploits low-rank tensor decompositions of potentially high-dimensional data sets to compute the corresponding DMD modes and eigenvalues. The goal is to reduce the computational complexity and also the amount of memory required to store the data in order to mitigate the curse of dimensionality. The efficiency of these tensor-based methods will be illustrated with the aid of several different fluid dynamics problems such as the von Kármán vortex street and the simulation of two merging vortices.

Original languageEnglish
Article number3359
JournalNonlinearity
Volume31
Issue number7
DOIs
Publication statusPublished - Jul 2018

Keywords

  • dynamic mode decomposition
  • pseudoinverse
  • tensor-train format

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy
  • Applied Mathematics

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