Tensor Dynamic Mode Decomposition

• URL: http://arxiv.org/abs/2508.02627v1
• Date: Mon, 04 Aug 2025 17:15:57 GMT
• Title: Tensor Dynamic Mode Decomposition
• Authors: Ziqin He, Mengqi Hu, Yifei Lou, Can Chen,
• Abstract summary: Dynamic mode decomposition (DMD) has become a powerful data-driven method for analyzing dynamics of complex, high-dimensional systems.<n>We propose tensor dynamic mode decomposition (TDMD), a extension of DMD to third-order tensors based on the recently developed T-product framework.<n>We demonstrate the effectiveness of TDMD on both synthetic and real-world datasets.
• Score: 7.9882756082182675
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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