用大模型同时评估方程的物理合理性和数值准确性，自动发现真实世界的微分方程。
Discovering Ordinary Differential Equations with LLM-Based Qualitative and Quantitative Evaluation
- 三代理架构：采样、优化、大模型评审，迭代搜索方程
- 在多维微分方程基准上成功率更高，更准确还原真实方程项
- 适合需要物理可解释性的科学建模场景，如生物、物理系统
从观测数据中发现控制微分方程是科学机器学习中的基础挑战。现有符号回归方法主要依赖定量指标；然而，真实世界建模还需融入领域知识以确保物理合理性。为此，我们提出DoLQ方法，通过大模型实现定性与定量联合评估来发现常微分方程。DoLQ采用多智能体架构：采样代理生成动力系统候选，参数优化器提升精度，科学家代理利用大模型进行定性与定量评估，并融合结果迭代引导搜索。在多维常微分方程基准上的实验表明，相比现有方法，DoLQ不仅取得更高成功率，还能更准确恢复真实方程的符号项。代码已开源：https://github.com/Bon99yun/DoLQ。
原文摘要 · Abstract (English)
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.
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