GAE: Graph-Augmented Evolution for Scientific Discovery via Reinforcement Optimization

Evolutionary program search guided by Large Language Models (LLMs) has emerged as a powerful paradigm for automated scientific discovery. However, current approaches are fundamentally constrained by three bottlenecks: structurally blind parent selection, sparse whole-program evaluation rewards, and static mutation operators that fail to adapt during search. We present \textbf{GAE} (\textbf{G}raph-\textbf{A}ugmented \textbf{E}volution), a framework that resolves these limitations through a tightly coupled, three-pillar architecture. First, a \textbf{relational graph neural network (GNN)} parses programs into typed computation graphs, producing structure-aware embeddings. Second, an \textbf{RL-optimized meta-controller} leverages these embeddings to replace blind evolutionary sampling with a directed policy, dynamically selecting optimal parents and mutation directions based on reward history. Third, an \textbf{online GRPO fine-tuning loop} continuously updates the LLM mutation operator at test-time using group-normalized evaluation rewards, directly aligning the model's generation distribution with high-fitness structural edits. We evaluate GAE on a challenging scientific discovery task: symbolic regression for complex nonlinear oscillator systems. By transforming stochastic search into a directed, self-improving trajectory, GAE efficiently discovers closed-form physical equations, consistently matching or outperforming static LLM-driven baselines and achieving state-of-the-art out-of-distribution performance.