LLM-ODE: Data-driven Discovery of Dynamical Systems with Large Language Models

TL;DR

LLM-ODE introduces a large language model-guided evolutionary framework for discovering dynamical system equations, significantly improving efficiency and accuracy over traditional genetic programming methods.

Contribution

The paper presents LLM-ODE, a novel LLM-aided symbolic evolution approach that enhances search efficiency and scalability in dynamical system discovery.

Findings

LLM-ODE outperforms classical GP in search efficiency.

LLM-ODE achieves higher Pareto-front quality.

The method scales better to higher-dimensional systems.

Abstract

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.