Discovering Ordinary Differential Equations with LLM-Based Qualitative and Quantitative Evaluation
For scientists modeling dynamical systems from data, DoLQ improves discovery of physically plausible ODEs by integrating domain knowledge via LLM-based evaluation.
DoLQ uses LLMs to qualitatively and quantitatively evaluate candidate ODEs, achieving higher success rates and more accurate symbolic term recovery on multi-dimensional benchmarks compared to existing methods.
Discovering governing differential equations from observational data is a fundamental challenge in scientific machine learning. Existing symbolic regression approaches rely primarily on quantitative metrics; however, real-world differential equation modeling also requires incorporating domain knowledge to ensure physical plausibility. To address this gap, we propose DoLQ, a method for discovering ordinary differential equations with LLM-based qualitative and quantitative evaluation. DoLQ employs a multi-agent architecture: a Sampler Agent proposes dynamic system candidates, a Parameter Optimizer refines equations for accuracy, and a Scientist Agent leverages an LLM to conduct both qualitative and quantitative evaluations and synthesize their results to iteratively guide the search. Experiments on multi-dimensional ordinary differential equation benchmarks demonstrate that DoLQ achieves superior performance compared to existing methods, not only attaining higher success rates but also more accurately recovering the correct symbolic terms of ground truth equations. Our code is available at https://github.com/Bon99yun/DoLQ.