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

• URL: http://arxiv.org/abs/2603.20910v1
• Date: Sat, 21 Mar 2026 18:46:38 GMT
• Title: LLM-ODE: Data-driven Discovery of Dynamical Systems with Large Language Models
• Abstract summary: Genetic programming (GP) has been widely adopted due to its flexibility and interpretability.<n>We propose LLM-ODE, a large language model-aided model discovery framework that guides symbolic evolution using patterns extracted from elite candidate equations.
• Score: 0.4419843514606336
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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