Tensor-based dynamic mode decomposition

TL;DR

This paper introduces a tensor-based extension of dynamic mode decomposition (DMD) that leverages low-rank tensor decompositions to analyze high-dimensional dynamical systems more efficiently, reducing computational costs and memory usage.

Contribution

It proposes a novel tensor-based DMD method that improves computational efficiency and scalability for high-dimensional data sets in dynamical systems analysis.

Findings

Tensor-based DMD reduces computational complexity.

The method efficiently analyzes fluid dynamics problems.

It mitigates the curse of dimensionality in DMD applications.

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.