Interpretable Relational Inference with LLM-Guided Symbolic Dynamics Modeling
For researchers studying many-body interacting systems, COSINE provides a method to infer interpretable interaction structures and dynamics without assuming known topology or fixed function libraries.
COSINE jointly discovers interaction graphs and sparse symbolic dynamics from observed dynamics, using an LLM to adaptively prune and expand the symbolic hypothesis space. It achieves robust structural recovery and compact, mechanism-aligned expressions on synthetic and real-world epidemic data.
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.