SR-LLM: An incremental symbolic regression framework driven by LLM-based retrieval-augmented generation

Area of Science:

• Artificial Intelligence
• Machine Learning
• Data Science

Background:

• Symbolic regression (SR) is crucial for discovering analytical models from data.
• Existing SR algorithms struggle with vast search spaces, limiting complex expression discovery.
• Deep learning advancements have renewed interest in SR for analytical modeling.

Purpose of the Study:

• To introduce SR-LLM, a novel SR framework leveraging large language models (LLM) and retrieval-augmented generation for incremental learning.
• To enhance the discovery of complex, interpretable analytical expressions by integrating prior knowledge.
• To apply the framework to challenging domains like human car-following behavior analysis.

Main Methods:

• SR-LLM integrates retrieval-augmented generation with LLMs for incremental learning.
• The framework composes prior information into symbolic groups using LLMs.
• Deep reinforcement learning combines these groups to formulate complex analytical expressions.

Main Results:

• SR-LLM demonstrates superior performance on standard SR benchmarks.
• The framework successfully rediscovers known car-following models from empirical data.
• New analytical models for human car-following behavior were discovered, showing both effectiveness and interpretability.

Conclusions:

• SR-LLM efficiently utilizes prior knowledge and past exploration for symbolic regression.
• The framework facilitates the discovery of complex, human-understandable analytical models.
• SR-LLM offers a powerful approach for scientific discovery in various domains, including behavioral analysis.