Data-driven model order reduction for T-Product-Based dynamical systems
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arXiv
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| Autori principali: | , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913801139388416 |
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| author | Mei, Shenghan He, Ziqin Mei, Yidan Mao, Xin Dong, Anqi Wang, Ren Chen, Can |
| author_facet | Mei, Shenghan He, Ziqin Mei, Yidan Mao, Xin Dong, Anqi Wang, Ren Chen, Can |
| contents | Model order reduction plays a crucial role in simplifying complex systems while preserving their essential dynamic characteristics, making it an invaluable tool in a wide range of applications, including robotic systems, signal processing, and fluid dynamics. However, traditional model order reduction techniques like balanced truncation are not designed to handle tensor data directly and instead require unfolding the data, which may lead to the loss of important higher-order structural information. In this article, we introduce a novel framework for data-driven model order reduction of T-product-based dynamical systems (TPDSs), which are often used to capture the evolution of third-order tensor data such as images and videos through the T-product. Specifically, we develop advanced T-product-based techniques, including T-balanced truncation, T-balanced proper orthogonal decomposition, and the T-eigensystem realization algorithm for input-output TPDSs by leveraging the unique properties of T-singular value decomposition. We demonstrate that these techniques offer significant memory and computational savings while achieving reduction errors that are comparable to those of conventional methods. The effectiveness of the proposed framework is further validated through synthetic and real-world examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14721 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Data-driven model order reduction for T-Product-Based dynamical systems Mei, Shenghan He, Ziqin Mei, Yidan Mao, Xin Dong, Anqi Wang, Ren Chen, Can Systems and Control Numerical Analysis Dynamical Systems 93C05, 15A69, 93B30, 65F99 Model order reduction plays a crucial role in simplifying complex systems while preserving their essential dynamic characteristics, making it an invaluable tool in a wide range of applications, including robotic systems, signal processing, and fluid dynamics. However, traditional model order reduction techniques like balanced truncation are not designed to handle tensor data directly and instead require unfolding the data, which may lead to the loss of important higher-order structural information. In this article, we introduce a novel framework for data-driven model order reduction of T-product-based dynamical systems (TPDSs), which are often used to capture the evolution of third-order tensor data such as images and videos through the T-product. Specifically, we develop advanced T-product-based techniques, including T-balanced truncation, T-balanced proper orthogonal decomposition, and the T-eigensystem realization algorithm for input-output TPDSs by leveraging the unique properties of T-singular value decomposition. We demonstrate that these techniques offer significant memory and computational savings while achieving reduction errors that are comparable to those of conventional methods. The effectiveness of the proposed framework is further validated through synthetic and real-world examples. |
| title | Data-driven model order reduction for T-Product-Based dynamical systems |
| topic | Systems and Control Numerical Analysis Dynamical Systems 93C05, 15A69, 93B30, 65F99 |
| url | https://arxiv.org/abs/2504.14721 |