LLMs Guide Scientific Equation Discovery via Search Control

Scientific equation discovery traditionally struggles with combining broad domain knowledge with strict numerical validation. This research explores a new division of labor, where large language models (LLMs) are used not to directly generate or choose equations, but to guide the search process for symbolic regression. The proposed system, LLM-PySR, allows LLMs to specify variables, operators, transformations, and search depth. Symbolic regression then enumerates and fits expressions, with deterministic metrics governing which equations are retained. This "search controller" approach was tested against various baselines, including end-to-end LLM systems and purely numerical methods, across 74 AI-Feynman equations and other complex formula-recovery tasks. LLM-PySR demonstrated superior balance in terms of accuracy, complexity, stability, and cost, even identifying a compact piecewise-linear relationship in an independent battery dataset.