SymBOL: A General-Purpose Symbolic Learner for Scientific Discovery Using Bayesian Optimization-Enhanced Large Language Models

Symbolic Regression (SR) is a core challenge in both physics and artificial intelligence, aiming to identify mathematical equations from experimental data. Recent impressive advancements in Large Language Model (LLM)-based SR methods have addressed the limitations of traditional approaches in flexibly incorporating prior knowledge to enhance accuracy, but they still face challenges such as high costs and scalability with numerous variables. To overcome these issues, we introduce SymBOL. This general-purpose symbolic learning framework uses Bayesian Optimization (BO) to guide the generation of high-quality mathematical expressions from the LLM while accommodating complex tasks with a large number of interdependent variables. Experiments on benchmark datasets demonstrate that SymBOL significantly outperforms baseline methods in both accuracy and efficiency. Notably, compared to advanced LLM-based approaches, SymBOL achieves a 24.85% improvement in average accuracy while reducing computational costs by 28.73%. This advantage extends to high-dimensional SR tasks, where SymBOL substantially lowers the average error. Furthermore, when applied to real-world systems in materials science and epidemiology, SymBOL accurately recovers governing equations and provides interpretable pathways for equation discovery. These findings underscore the potential of SymBOL for advancing scientific discovery.