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

2026-03-21

AI Summary

Traditional genetic programming faces significant challenges in discovering governing equations of dynamical systems, including low search efficiency, slow convergence, and poor solution quality. This work proposes LLM-ODE, a novel framework that, for the first time, integrates the generative priors of large language models into symbolic regression. By extracting structural patterns from elite candidate equations, LLM-ODE effectively guides the symbolic evolution process of genetic programming, substantially enhancing both search efficiency and solution accuracy while preserving exploratory capability. Experimental evaluation across 91 dynamical systems demonstrates that LLM-ODE consistently outperforms conventional genetic programming, linear methods, and pure Transformer-based models in terms of search efficiency, Pareto front quality, and scalability to high-dimensional systems.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Natural Language Processing: Code Generation / Program Synthesis from Natural Language
• Machine Learning: Large Multimodal Models (LMMs)

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• dynamical systems
• equation discovery
• symbolic regression
• genetic programming
• large language models

Innovation

• large language models
• symbolic regression
• genetic programming
• dynamical systems discovery
• data-driven modeling