arXiv：cs.LG· Kaiming Luo·· 7 小时前AI 评分35
变分物理信息拟设：从稳态观测重建隐藏交互网络
Variational Physics-Informed Ansatz for Reconstructing Hidden Interaction Networks from Steady States
AI 导读
研究者提出一种变分物理信息拟设（variational physics-informed ansatz），将未知交互算子表示为可训练对象，通过最小化多次异质扰动实验的稳态残差来重建隐藏交互网络。在仿射交互设定下，堆叠的平衡方程给出显式有限样本可辨识条件：消除逐实验规范自由度后，唯一恢复由兼容矩阵的秩决定。在成对、有向、加权、经验拓扑及部分高阶系统上的合成基准验证了该可辨识性图景。
正文
Abstract:Inferring interaction structure from steady-state observations is a central inverse problem when transient trajectories are unavailable. Here we formulate this problem as simultaneous compatibility of a single interaction operator with equilibrium constraints generated by heterogeneous perturbations. We introduce a variational physics-informed ansatz that represents the unknown operator as a trainable object and minimizes the resulting steady-state residuals across experiments. In the affine-interaction setting, the stacked equilibrium equations yield explicit finite-sample identifiability conditions: unique recovery is controlled by the rank of the compatibility matrix after elimination of experiment-wise gauge freedom. Synthetic benchmarks on pairwise, directed, weighted, empirical-topology, and selected higher-order systems illustrate this identifiability picture and show how additional heterogeneous steady states improve structural discrimination under the stated assumptions. The results clarify a concrete steady-state reconstruction regime in which equilibrium observations alone can determine hidden interaction operators when the governing dynamics are known and node-level equilibria are fully observed.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2512.13708 [cs.LG] |
| (or arXiv:2512.13708v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2512.13708 arXiv-issued DOI via DataCite |
Submission history
From: Kaiming Luo [view email]
[v1]
Sat, 6 Dec 2025 08:16:32 UTC (1,270 KB)
[v2]
Tue, 6 Oct 2026 03:24:18 UTC (1,497 KB)
来源：arXiv：cs.LG · arxiv.org