Tensor-based dynamic mode decomposition
For researchers analyzing complex dynamical systems, this provides a more efficient DMD approach for high-dimensional data, though it is an incremental extension.
The paper extends dynamic mode decomposition (DMD) to handle high-dimensional data using low-rank tensor decompositions, reducing computational and memory costs. The method is demonstrated on fluid dynamics problems like the von Kármán vortex street.
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.