# Tensor Dynamic Mode Decomposition

arXiv: https://arxiv.org/abs/2508.02627 · HTML: https://mlsanity.com/paper/2508.02627/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 36 references that are in the map.
- First posted on arXiv 4 Aug 2025.

## Builds on (most cited first, 8 of 8)

- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [Dynamic mode decomposition with control](https://mlsanity.com/paper/1409.6358/) (2014)
- [Exact tensor completion using t-SVD](https://mlsanity.com/paper/1502.04689/) (2015)
- [Extracting spatial-temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition](https://mlsanity.com/paper/1409.5496/) (2014)
- [Tensor-Tensor Product Toolbox](https://mlsanity.com/paper/1806.07247/) (2018)
- [Three-dimensional signal processing: a new approach in dynamical sampling via tensor products](https://mlsanity.com/paper/2502.02684/) (2025)
- [Explicit Solutions and Stability Properties of Homogeneous Polynomial Dynamical Systems](https://mlsanity.com/paper/2107.11438/) (2021)
- [Data-driven Analysis of T-Product-based Dynamical Systems](https://mlsanity.com/paper/2410.20541/) (2024)

## Abstract (arXiv)

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.