Tensor-based homogeneous polynomial dynamical system analysis from data
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909549206700032 |
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| author | Mao, Xin Dong, Anqi He, Ziqin Mei, Yidan Mei, Shenghan Chen, Can |
| author_facet | Mao, Xin Dong, Anqi He, Ziqin Mei, Yidan Mei, Shenghan Chen, Can |
| contents | Numerous complex real-world systems, such as those in biological, ecological, and social networks, exhibit higher-order interactions that are often modeled using polynomial dynamical systems or homogeneous polynomial dynamical systems (HPDSs). However, identifying system parameters and analyzing key system-theoretic properties remain challenging due to their inherent nonlinearity and complexity, particularly for large-scale systems. To address these challenges, we develop an innovative computational framework in this article that leverages advanced tensor decomposition techniques, namely tensor train and hierarchical Tucker decompositions, to facilitate efficient identification and analysis of HPDSs that can be equivalently represented by tensors. Specifically, we introduce memory-efficient system identification techniques for directly estimating system parameters represented through tensor decompositions from time-series data. Additionally, we develop necessary and sufficient conditions for determining controllability and observability using the tensor decomposition-based representations of HPDSs, accompanied by detailed complexity analyses that demonstrate significant reductions in computational demands. The effectiveness and efficiency of our framework are validated through numerical examples. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_17774 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tensor-based homogeneous polynomial dynamical system analysis from data Mao, Xin Dong, Anqi He, Ziqin Mei, Yidan Mei, Shenghan Chen, Can Dynamical Systems Systems and Control Optimization and Control 15A69, 53A45, 93B05, 93B07, 93B40, 93C15, 93D05 Numerous complex real-world systems, such as those in biological, ecological, and social networks, exhibit higher-order interactions that are often modeled using polynomial dynamical systems or homogeneous polynomial dynamical systems (HPDSs). However, identifying system parameters and analyzing key system-theoretic properties remain challenging due to their inherent nonlinearity and complexity, particularly for large-scale systems. To address these challenges, we develop an innovative computational framework in this article that leverages advanced tensor decomposition techniques, namely tensor train and hierarchical Tucker decompositions, to facilitate efficient identification and analysis of HPDSs that can be equivalently represented by tensors. Specifically, we introduce memory-efficient system identification techniques for directly estimating system parameters represented through tensor decompositions from time-series data. Additionally, we develop necessary and sufficient conditions for determining controllability and observability using the tensor decomposition-based representations of HPDSs, accompanied by detailed complexity analyses that demonstrate significant reductions in computational demands. The effectiveness and efficiency of our framework are validated through numerical examples. |
| title | Tensor-based homogeneous polynomial dynamical system analysis from data |
| topic | Dynamical Systems Systems and Control Optimization and Control 15A69, 53A45, 93B05, 93B07, 93B40, 93C15, 93D05 |
| url | https://arxiv.org/abs/2503.17774 |