用大模型辅助符号推演，自动发现复杂系统的隐藏互动关系
Interpretable Relational Inference with LLM-Guided Symbolic Dynamics Modeling
- 联合优化符号动力学与交互图结构，实现可解释的系统建模
- 在合成数据和真实疫情数据上均实现高精度结构恢复
- 适合需要理解机制而非黑箱预测的科学建模场景
从观测动态中推断多体相互作用系统的潜在交互结构是基础性逆问题。现有神经方法依赖可训练图的黑箱代理，虽准确但缺乏机制可解释性；符号回归能给出显式动力学方程并具备更强归纳偏置，但通常假设拓扑已知且函数库固定。本文提出COSINE（Co-Optimization of Symbolic Interactions and Network Edges），一种可微分框架，联合发现交互图与稀疏符号动力学。为克服固定符号库的限制，COSINE进一步引入外层大语言模型，通过内层优化反馈自适应剪枝与扩展假设空间。在合成系统和大规模真实疫情数据上的实验表明，该方法能稳健恢复系统结构，并生成简洁、机制对齐的动力学表达式。代码：https://anonymous.4open.science/r/COSINE-6D43。
原文摘要 · Abstract (English)
Inferring latent interaction structures from observed dynamics is a fundamental inverse problem in many-body interacting systems. Most neural approaches rely on black-box surrogates over trainable graphs, achieving accuracy at the expense of mechanistic interpretability. Symbolic regression offers explicit dynamical equations and stronger inductive biases, but typically assumes known topology and a fixed function library. We propose \textbf{COSINE} (\textbf{C}o-\textbf{O}ptimization of \textbf{S}ymbolic \textbf{I}nteractions and \textbf{N}etwork \textbf{E}dges), a differentiable framework that jointly discovers interaction graphs and sparse symbolic dynamics. To overcome the limitations of fixed symbolic libraries, COSINE further incorporates an outer-loop large language model that adaptively prunes and expands the hypothesis space using feedback from the inner optimization loop. Experiments on synthetic systems and large-scale real-world epidemic data demonstrate robust structural recovery and compact, mechanism-aligned dynamical expressions. Code: https://anonymous.4open.science/r/COSINE-6D43.
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