SR-Scientist: Scientific Equation Discovery With Agentic AI

TL;DR

SR-Scientist reframes symbolic regression as an autonomous, long-horizon scientific discovery task by equipping LLM agents with tool-driven data analysis and equation evaluation. The framework wraps a code-interpreter into data-analyzer and equation-evaluator tools, augmented by an experience buffer and reinforcement learning to evolve discovery strategies across multiple disciplines. Empirical results across four domains show consistent accuracy gains (up to $6\%$–$35\%$ absolute) over baselines, with strong generalization to out-of-domain data and resilience to noise, alongside improved symbolic accuracy. The work also provides an end-to-end RL pipeline to further enhance the agent's capabilities and demonstrates practical feasibility with multiple backbone LLMs.

Abstract

Recently, Large Language Models (LLMs) have been applied to scientific equation discovery, leveraging their embedded scientific knowledge for hypothesis generation. However, current methods typically confine LLMs to the role of an equation proposer within search algorithms like genetic programming. In this paper, we present SR-Scientist, a framework that elevates the LLM from a simple equation proposer to an autonomous AI scientist that writes code to analyze data, implements the equation as code, submits it for evaluation, and optimizes the equation based on experimental feedback. Specifically, we wrap the code interpreter into a set of tools for data analysis and equation evaluation. The agent is instructed to optimize the equation by utilizing these tools over a long horizon with minimal human-defined pipelines. Empirical results show that SR-Scientist outperforms baseline methods by an absolute margin of 6% to 35% on datasets covering four science disciplines. Additionally, we demonstrate our method's robustness to noise, the generalization of the discovered equations to out-of-domain data, and their symbolic accuracy. Furthermore, we develop an end-to-end reinforcement learning framework to enhance the agent's capabilities.

Figures (17)

• Figure 1: The inference framework of SR-Scientist. At each iteration, the LLM agent autonomously conducts long-horizon optimization using code interpreters for data analysis and equation evaluation. To overcome the context length limitations of current LLMs, we implement an experience buffer to fetch the best-performing equations for subsequent iterations. 'Eq' denotes the equation and 'S' denotes the equation score.
• Figure 2: Detailed results of in-domain (ID) and out-of-domain (OOD) performance using $\text{Acc}_{0.01}$ across various LSR-Synth scientific domains. (with Qwen3-Coder-480B as LLM backbone)
• Figure 3: Noise robustness analysis. Qwen, GLM, and GPT represent Qwen3-Coder-480B, GLM-4.5-Air, and GPT-OSS-120B, respectively.
• Figure 4: Overall performance under different maximum turns. We keep the total number of LLM calls at around 1,000 and trade off between maximum turns and iterations.
• Figure 5: Equations discovered for the PO10 and PO37 physics problems. The variables $\dot{v}(t)$, $t$, $x$, and $v$ represent acceleration in a non-linear harmonic oscillator, time, position, and velocity, respectively. Terms highlighted in green are common to both the predicted and ground truth equations.