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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.20910 |
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| _version_ | 1866908935887257600 |
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| author | Bideh, Amirmohammad Ziaei Gryak, Jonathan |
| author_facet | Bideh, Amirmohammad Ziaei Gryak, Jonathan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20910 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | LLM-ODE: Data-driven Discovery of Dynamical Systems with Large Language Models Bideh, Amirmohammad Ziaei Gryak, Jonathan Machine Learning 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. |
| title | LLM-ODE: Data-driven Discovery of Dynamical Systems with Large Language Models |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2603.20910 |