Automated Algorithmic Discovery for Scientific Computing through LLM-Guided Evolutionary Search: A Case Study in Gravitational-Wave Detection

Automated algorithm discovery in scientific computing faces fundamental challenges: vast design spaces with expensive evaluations, domain-specific physical constraints requiring expert knowledge, and the necessity for interpretable solutions that scientists can validate and understand. We present the Evo-MCTS (Evolutionary Monte Carlo Tree Search) framework, integrating large language models (LLMs) with tree-structured evolutionary search for interpretable algorithm discovery. Evo-MCTS combines reflective code synthesis leveraging LLM domain knowledge, multi-scale evolutionary operations on structured code representations, and interpretable algorithmic pathways emerging from tree-guided exploration. When applied to gravitational wave detection-a challenging domain with continuous parameter spaces and strict physical constraints-Evo-MCTS achieves 20.2% improvement over domain-specific methods and 59.1% over LLM-based optimization frameworks. This improvement arises from its ability to consistently converge toward interpretable algorithmic structures that integrate multiple functional components. Our domain-agnostic architecture establishes a generalizable methodology for automated algorithm discovery in scientific computing, where algorithmic transparency and physical validity are as essential as performance optimization.