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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2512.13708 |
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| _version_ | 1866918249535373312 |
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| author | Luo, Kaiming |
| author_facet | Luo, Kaiming |
| contents | The interaction structure of a complex dynamical system governs its collective behavior, yet existing reconstruction methods struggle with nonlinear, heterogeneous, and higher-order couplings, especially when only steady states are observable. We propose a Variational Physics-Informed Ansatz (VPIA) that infers general interaction operators directly from heterogeneous steady-state data. VPIA embeds the steady-state constraints of the dynamics into a differentiable variational representation and reconstructs the underlying couplings by minimizing a physics-derived steady-state residual, without requiring temporal trajectories, derivative estimation, or supervision. Residual sampling combined with natural-gradient optimization enables scalable learning of large and higher-order networks. Across diverse nonlinear systems, VPIA accurately recovers directed, weighted, and multi-body structures under substantial noise, providing a unified and robust framework for physics-constrained inference of complex interaction networks in settings where only snapshot observations are available. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13708 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Variational Physics-Informed Ansatz for Reconstructing Hidden Interaction Networks from Steady States Luo, Kaiming Machine Learning The interaction structure of a complex dynamical system governs its collective behavior, yet existing reconstruction methods struggle with nonlinear, heterogeneous, and higher-order couplings, especially when only steady states are observable. We propose a Variational Physics-Informed Ansatz (VPIA) that infers general interaction operators directly from heterogeneous steady-state data. VPIA embeds the steady-state constraints of the dynamics into a differentiable variational representation and reconstructs the underlying couplings by minimizing a physics-derived steady-state residual, without requiring temporal trajectories, derivative estimation, or supervision. Residual sampling combined with natural-gradient optimization enables scalable learning of large and higher-order networks. Across diverse nonlinear systems, VPIA accurately recovers directed, weighted, and multi-body structures under substantial noise, providing a unified and robust framework for physics-constrained inference of complex interaction networks in settings where only snapshot observations are available. |
| title | Variational Physics-Informed Ansatz for Reconstructing Hidden Interaction Networks from Steady States |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2512.13708 |