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.

翻译：从观测数据中发现控制微分方程是科学机器学习中的一个基础挑战。现有的符号回归方法主要依赖定量指标；然而，真实世界中的微分方程建模还需要融入领域知识以确保物理合理性。为解决这一问题，我们提出DoLQ方法——一种基于大语言模型进行定性与定量评估的常微分方程发现方法。DoLQ采用多智能体架构：采样智能体负责提出动态系统候选方案，参数优化器通过调整参数提高方程精度，科学家智能体则利用大语言模型同时进行定性与定量评估，并综合其结果迭代指导搜索过程。在多维常微分方程基准测试上的实验表明，相比现有方法，DoLQ不仅取得了更高的成功率，还能更准确地恢复真实方程的正确符号项。我们的代码开源在 https://github.com/Bon99yun/DoLQ。