Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Amirmohammad Ziaei Bideh, Jonathan Gryak

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.

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

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.
Paper Structure (7 sections, 7 equations, 1 figure, 3 algorithms)

This paper contains 7 sections, 7 equations, 1 figure, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. Problem Statement
  5. Overview of LLM-ODE
  6. Experiments
  7. LLM-ODE Setup

Figures (1)

  • Figure 1: Schematic overview of LLM-ODE. (1) Given trajectory data from an unknown dynamical system, the observations are decomposed into state variables. (2) A large language model acts as an evolutionary operator, guiding the evolution of symbolic equation populations toward higher-fitness candidates. (3) The final system of equations is selected from the Cartesian product of equation-level Pareto fronts.