Tensor-based dynamic mode decomposition
Numerical Analysis
2019-08-14 v2 Dynamical Systems
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 K\'arm\'an vortex street and the simulation of two merging vortices.
Keywords
Cite
@article{arxiv.1606.06625,
title = {Tensor-based dynamic mode decomposition},
author = {Stefan Klus and Patrick Gelß and Sebastian Peitz and Christof Schütte},
journal= {arXiv preprint arXiv:1606.06625},
year = {2019}
}