用大模型加速科学方程发现，比传统方法更快更准
LLM-ODE: Data-driven Discovery of Dynamical Systems with Large Language Models
- 用大模型提取优秀方程模式，指导符号演化搜索
- 91个系统测试中，搜索效率与解的质量均超越经典遗传编程
- 适合需要快速发现复杂动力系统方程的研究者
发现动力系统的控制方程是众多科学领域的核心问题。随着实验数据日益丰富，基于数据的自动化方程发现方法为加速科学发现提供了可能。其中，遗传编程（GP）因其灵活性和可解释性被广泛采用，但常因符号搜索空间探索效率低，导致收敛慢、解不优。为此，我们提出LLM-ODE——一种利用大语言模型引导符号演化的模型发现框架，通过提取优质候选方程中的模式，生成更智能的搜索路径。在91个动力系统上的实证结果表明，LLM-ODE变体在搜索效率和帕累托前沿质量上均持续优于传统GP方法。整体结果表明，相比传统GP，LLM-ODE在效率与精度上均有提升，并且在高维系统上比线性及仅依赖Transformer的方法更具可扩展性。
原文摘要 · Abstract (English)
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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