GAE Enhances Scientific Discovery with Graph-Augmented LLM Evolution

Automated scientific discovery, particularly through evolutionary program search guided by Large Language Models (LLMs), holds immense promise but faces several inherent challenges. Existing methods often suffer from blind parent selection, sparse reward signals for whole programs, and static mutation operators that fail to adapt during the search process. This research introduces GAE (Graph-Augmented Evolution), a comprehensive framework designed to overcome these bottlenecks. GAE operates on a three-pillar architecture. First, it employs a relational graph neural network (GNN) to transform programs into typed computation graphs, generating embeddings that are deeply aware of the program's underlying structure. Second, an RL-optimized meta-controller utilizes these structural embeddings to guide the evolutionary process, replacing random sampling with a directed policy for selecting optimal parents and mutation directions based on historical reward data. Finally, GAE incorporates an online GRPO fine-tuning loop that continuously updates the LLM's mutation operator during test-time. This dynamic adaptation uses group-normalized evaluation rewards to align the LLM's generation distribution directly with structural edits that lead to high-fitness outcomes. Tested on symbolic regression for complex nonlinear oscillator systems, GAE efficiently discovers closed-form physical equations, consistently outperforming static LLM-driven baselines and achieving state-of-the-art out-of-distribution performance.