Tensor Dynamic Mode Decomposition

TL;DR

Tensor Dynamic Mode Decomposition (TDMD) extends traditional DMD to multidimensional tensor data, enabling more efficient analysis of complex spatiotemporal systems with improved structure preservation.

Contribution

TDMD introduces a tensor-based extension of DMD using T-product framework, enhancing computational efficiency and structural fidelity for high-dimensional data analysis.

Findings

TDMD outperforms standard DMD in state reconstruction.

TDMD better preserves spatial and temporal structures.

Effective on both synthetic and real-world datasets.

Abstract

Dynamic mode decomposition (DMD) has become a powerful data-driven method for analyzing the spatiotemporal dynamics of complex, high-dimensional systems. However, conventional DMD methods are limited to matrix-based formulations, which might be inefficient or inadequate for modeling inherently multidimensional data including images, videos, and higher-order networks. In this letter, we propose tensor dynamic mode decomposition (TDMD), a novel extension of DMD to third-order tensors based on the recently developed T-product framework. By incorporating tensor factorization techniques, TDMD achieves more efficient computation and better preservation of spatial and temporal structures in multiway data for tasks such as state reconstruction and dynamic component separation, compared to standard DMD with data flattening. We demonstrate the effectiveness of TDMD on both synthetic and real-world datasets.