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

Jianke Yang, Ohm Venkatachalam, Mohammad Kianezhad, Sharvaree Vadgama, Rose Yu · Feb 12, 2026 · Citations: 0

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.

Human Data Lens

Uses human feedback: No
Feedback types: None
Rater population: Unknown
Unit of annotation: Unknown
Expertise required: General

Evaluation Lens

Evaluation modes: Automatic Metrics
Agentic eval: Long Horizon
Quality controls: Not reported
Confidence: 0.45
Flags: ambiguous

Research Summary

Contribution Summary

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

Why It Matters For Eval

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.