Official implementation of paper LLM-ODE: Data-driven Discovery of Dynamical Systems with Large Language Models (GECCO 2026)
Genetic programming (GP) is an established approach for automated equation discovery but suffers from inefficient search and slow convergence. LLM-ODE addresses this by using an LLM as a genetic variation operator that extracts patterns from elite candidate equations to guide symbolic evolution more effectively. Evaluated on 91 dynamical systems, LLM-ODE consistently outperforms standard GP baselines in search efficiency and solution quality, with stronger scalability to high-dimensional systems than linear or Transformer-only methods.
First, you need to install the dependencies:
git clone git@github.com:gryaklab/llm-ode.git
cd llmode
uv sync
The script serve_and_run.sh launches the vllm servers in the background and runs LLM-ODE on all datasets:
chmod +x serve_and_run.sh
./serve_and_run.sh
In separate environments, you need to install the required packages for each baseline method. Then, issue:
python -m baselines.pysr --save_dir results/pysr/
python -m baselines.sindy --save_dir results/sindy/
python -m baselines.odeformer --save_dir results/odeformer/
Issue uv run pytest.
If you find our work useful, consider a ⭐️ and citing us with
@article{bideh2026llmode,
title={LLM-ODE: Data-driven Discovery of Dynamical Systems with Large Language Models},
author={Bideh, Amirmohammad Ziaei and Gryak, Jonathan},
journal={arXiv preprint arXiv:2603.20910},
year={2026}
}This project is licensed under the MIT License. See the LICENSE file for details.