In Context Learning and Reasoning for Symbolic Regression with Large Language Models

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Abstract

Large Language Models (LLMs) are transformer-based machine learning models that have shown remarkable performance in tasks for which they were not explicitly trained. Here, we explore the potential of LLMs to perform symbolic regression -- a machine-learning method for finding simple and accurate equations from datasets. We prompt GPT-4 and GPT-4o models to suggest expressions from data, which are then optimized and evaluated using external Python tools. These results are fed back to the LLMs, which propose improved expressions while optimizing for complexity and loss. Using chain-of-thought prompting, we instruct the models to analyze data, prior expressions, and the scientific context (expressed in natural language) for each problem before generating new expressions. We evaluated the workflow in rediscovery of Langmuir and dual-site Langmuir's model for adsorption, along with Nikuradse's dataset on flow in rough pipes, which does not have a known target model equation. Both the GPT-4 and GPT-4o models successfully rediscovered equations, with better performance when using a scratchpad and considering scientific context. GPT-4o model demonstrated improved reasoning with data patterns, particularly evident in the dual-site Langmuir and Nikuradse dataset. We demonstrate how strategic prompting improves the model's performance and how the natural language interface simplifies integrating theory with data. We also applied symbolic mathematical constraints based on the background knowledge of data via prompts and found that LLMs generate meaningful equations more frequently. Although this approach does not outperform established SR programs where target equations are more complex, LLMs can nonetheless iterate toward improved solutions while following instructions and incorporating scientific context in natural language.