LLM4ED: Large Language Models for Automatic Equation Discovery
This work addresses the challenge of equation discovery for researchers and practitioners by lowering barriers to applying these techniques, though it is incremental as it builds on existing symbolic methods with LLM integration.
The authors tackled the problem of automatically extracting physical laws from data by introducing a framework that uses natural language prompts to guide large language models (LLMs) in discovering governing equations, achieving effective equation discovery across various nonlinear dynamic systems with good stability and usability compared to state-of-the-art models.
Equation discovery is aimed at directly extracting physical laws from data and has emerged as a pivotal research domain. Previous methods based on symbolic mathematics have achieved substantial advancements, but often require the design of implementation of complex algorithms. In this paper, we introduce a new framework that utilizes natural language-based prompts to guide large language models (LLMs) in automatically mining governing equations from data. Specifically, we first utilize the generation capability of LLMs to generate diverse equations in string form, and then evaluate the generated equations based on observations. In the optimization phase, we propose two alternately iterated strategies to optimize generated equations collaboratively. The first strategy is to take LLMs as a black-box optimizer and achieve equation self-improvement based on historical samples and their performance. The second strategy is to instruct LLMs to perform evolutionary operators for global search. Experiments are extensively conducted on both partial differential equations and ordinary differential equations. Results demonstrate that our framework can discover effective equations to reveal the underlying physical laws under various nonlinear dynamic systems. Further comparisons are made with state-of-the-art models, demonstrating good stability and usability. Our framework substantially lowers the barriers to learning and applying equation discovery techniques, demonstrating the application potential of LLMs in the field of knowledge discovery.