Think like a Scientist: Physics-guided LLM Agent for Equation Discovery

TL;DR

KeplerAgent is a physics-guided LLM framework that mimics scientific reasoning by inferring physical properties before discovering equations, leading to more accurate and robust symbolic discovery.

Contribution

It introduces KeplerAgent, a novel framework that integrates physics-based reasoning with symbolic regression, improving equation discovery over existing LLM-based methods.

Findings

Achieves higher symbolic accuracy on physical benchmarks.

Demonstrates robustness to noisy data.

Outperforms traditional and LLM-based baselines.

Abstract

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.