[2603.20910] LLM-ODE: Data-driven Discovery of Dynamical Systems with Large Language Models

Computer Science > Machine Learning arXiv:2603.20910 (cs) [Submitted on 21 Mar 2026] Title:LLM-ODE: Data-driven Discovery of Dynamical Systems with Large Language Models Authors:Amirmohammad Ziaei Bideh, Jonathan Gryak View a PDF of the paper titled LLM-ODE: Data-driven Discovery of Dynamical Systems with Large Language Models, by Amirmohammad Ziaei Bideh and 1 other authors View PDF HTML (experimental) 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-fr...