让大模型像科学家一样分步推导物理方程，提升准确性和抗噪能力。
Think like a Scientist: Physics-guided LLM Agent for Equation Discovery
- 模拟科学家思维：先推导对称性等物理特性，再约束方程搜索空间。
- 在多个物理方程基准上，符号准确率显著优于传统方法和普通LLM。
- 适合需要可解释方程的科研场景，如力学、电磁学建模。
通过符号化、可解释的公式来解释观测现象是科学的核心目标。近年来，大型语言模型（LLMs）因其广泛的领域知识和强大的推理能力，成为符号方程发现的有力工具。然而，大多数现有基于LLM的系统直接从数据中猜测方程，未建模科学家常采用的多步推理过程：首先推断对称性等物理属性，再以此作为先验限制候选方程空间。我们提出KeplerAgent，一种遵循该科学推理流程的智能体框架。该智能体协调基于物理的工具提取中间结构，并利用这些结果配置符号回归引擎（如PySINDy和PySR），包括函数库与结构约束。在一系列物理方程基准测试中，KeplerAgent在符号准确率和对噪声数据的鲁棒性方面均显著优于LLM及传统基线方法。
原文摘要 · Abstract (English)
Explaining observed phenomena through symbolic, interpretable formulas is a fundamental goal of science. Recently, large language models (LLMs) have emerged as promising tools for symbolic equation discovery, owing to their broad domain knowledge and strong reasoning capabilities. However, most existing LLM-based systems try to guess equations directly from data, without modeling the multi-step reasoning process that scientists often follow: first inferring physical properties such as symmetries, then using these as priors to restrict the space of candidate equations. We introduce KeplerAgent, an agentic framework that explicitly follows this scientific reasoning process. The agent coordinates physics-based tools to extract intermediate structure and uses these results to configure symbolic regression engines such as PySINDy and PySR, including their function libraries and structural constraints. Across a suite of physical equation benchmarks, KeplerAgent achieves substantially higher symbolic accuracy and greater robustness to noisy data than both LLM and traditional baselines.
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