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arXiv · 2604.12806

Interpretable Relational Inference with LLM-Guided Symbolic Dynamics Modeling

Xiaoxiao Liang·Juyuan Zhang·Liming Pan·Linyuan Lü
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Abstract

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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Xiaoxiao Liang, Juyuan Zhang, Liming Pan, Linyuan Lü. 2026-04-14. Interpretable Relational Inference with LLM-Guided Symbolic Dynamics Modeling. https://arxiv.org/abs/2604.12806

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