Evolutionary Identification of Scientific Equations Using Language-Model-Guided Symbolic Regression

Abstract

Symbolic Regression (SR) is a central problem in evolutionary computation concerned with identifying symbolic equations from data. In many scientific and engineering settings, observed data are governed by physical laws drawn from known but implicitly defined families of equations, where the exact symbolic form is unknown and difficult to enumerate a priori. In such settings, exact structural identification is more critical than arbitrary function approximation. We present an evolutionary SR approach for scientific equation identification in which large language models (LLMs) are integrated directly into the evolutionary process as guided variation operators. The method maintains a population of candidate symbolic expressions and evolves them over successive generations using fitness-based selection, structural diversity preservation, and stateful evolutionary memory. LLM guidance proposes structurally informed variations that exploit qualitative prior knowledge while remaining embedded within an evolutionary search framework. We evaluate the approach on the SRSD-Feynman benchmark, demonstrating robust rediscovery of scientific equations across easy and medium difficulty subsets, with competitive performance on harder instances. Results show that incorporating language-model guidance into evolutionary SR substantially improves search efficiency while preserving interpretability and the evolutionary character of the algorithm.