从稳态数据中重建复杂系统的隐藏耦合网络，无需时间序列。
Variational Physics-Informed Ansatz for Reconstructing Hidden Interaction Networks from Steady States
- 基于变分物理约束框架，直接从稳态数据推断耦合关系。
- 在强噪声下仍能准确恢复有向、加权及多体耦合结构。
- 适合仅能观测快照的复杂系统建模，如生物或社会网络。
复杂动力系统的相互作用结构决定了其集体行为，但现有重构方法难以处理非线性、异质性及高阶耦合，尤其在仅有稳态可观测时。我们提出变分物理信息构型（VPIA），直接从异质稳态数据中推断通用相互作用算子。VPIA将动态系统的稳态约束嵌入可微分的变分表示中，通过最小化物理导出的稳态残差来重构底层耦合，无需时间轨迹、导数估计或监督信号。残差采样结合自然梯度优化实现大规模和高阶网络的可扩展学习。在多种非线性系统中，VPIA在显著噪声下仍能准确恢复有向、加权及多体结构，为仅能获取快照观测的场景提供了统一且鲁棒的物理约束推理框架。
原文摘要 · Abstract (English)
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.
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