LLM-ODE: Data-driven Discovery of Dynamical Systems with Large Language Models
This addresses a bottleneck in automated equation discovery for scientific disciplines, offering incremental improvements in efficiency and scalability over existing methods.
The paper tackles the problem of inefficient exploration in genetic programming for discovering governing equations of dynamical systems, proposing LLM-ODE, which uses large language models to guide symbolic evolution. Empirical results on 91 systems show it outperforms classical GP methods in search efficiency and Pareto-front quality.
Discovering the governing equations of dynamical systems is a central problem across many scientific disciplines. As experimental data become increasingly available, automated equation discovery methods offer a promising data-driven approach to accelerate scientific discovery. Among these methods, genetic programming (GP) has been widely adopted due to its flexibility and interpretability. However, GP-based approaches often suffer from inefficient exploration of the symbolic search space, leading to slow convergence and suboptimal solutions. To address these limitations, we propose LLM-ODE, a large language model-aided model discovery framework that guides symbolic evolution using patterns extracted from elite candidate equations. By leveraging the generative prior of large language models, LLM-ODE produces more informed search trajectories while preserving the exploratory strengths of evolutionary algorithms. Empirical results on 91 dynamical systems show that LLM-ODE variants consistently outperform classical GP methods in terms of search efficiency and Pareto-front quality. Overall, our results demonstrate that LLM-ODE improves both efficiency and accuracy over traditional GP-based discovery and offers greater scalability to higher-dimensional systems compared to linear and Transformer-only model discovery methods.