SR-Scientist: Scientific Equation Discovery With Agentic AI

Key points

• Problem: Current LLM-based symbolic regression (finding equations from data) typically confines the LLM to the role of an equation proposer inside search algorithms such as genetic programming. These hybrid methods lack direct analysis of observed data through tools, and the LLM's behavior is often fixed. Most work focuses on using LLMs for inference, leaving open how RL could grow the models' abilities.
• Input and output: This paper implements and tests an agent framework for equation discovery. The input is the observed data of one scientific scenario (input variables and output values), and the output is the equation, written as a Python function with constant placeholders, that fits the observed data best. Evaluation uses the 129 problems of LSR-Synth, the synthetic part of LLM-SRBench (36 chemistry, 24 biology, 44 physics, 25 materials science), which mix known terms with new synthetic terms so that LLMs cannot rely on memorized equations.
• Method: The agent gets two tools that wrap a code interpreter: a data analyzer for free-form data analysis and an equation evaluator that takes an equation skeleton (an equation with placeholder constants), fits the constants with BFGS (Broyden-Fletcher-Goldfarb-Shanno, a numerical optimizer), and reports the error. In each iteration the agent repeats data analysis and equation edits for up to 25 turns (40 iterations in total in the experiments), and an experience buffer stores explored equations with their MAPE (mean absolute percentage error) so the top K return at the start of the next iteration. Training runs GRPO (Group Relative Policy Optimization) RL on 1024 synthesized problems, turning the MAPE of the best equation found into a log-linear reward.
• Implementation: The five main inference backbones are Qwen3-Coder-480B-A35B, GLM-4.5-Air, GPT-OSS-120B, GPT-OSS-20B, and Qwen3-Coder-30B-A3B, and among them RL training was done only on Qwen3-Coder-30B because of compute cost and training infrastructure limits, for 60 steps on 32 H200 GPUs with the verl framework. In the appendix, the authors also ran RL with the same training configuration on Qwen3-8B, Qwen3-14B, and Qwen3-32B. The README of the GitHub repository releases the inference framework and the RL training framework, links the trained SR-Scientist-30B model and the training dataset on Hugging Face, and has users install SandboxFusion separately as the code execution sandbox.
• Results: On Acc0.01 over all 129 problems (share of problems whose test points, after dropping the worst 5%, all fall within 1% relative error), SR-Scientist with GPT-OSS-120B scored 63.57%, the highest of all method and backbone pairs in Table 1, while LLM-SR, a baseline where the LLM proposes equations, scored 28.16% with the same backbone. The authors report absolute margins of 6% to 35% over baselines for four of the five main backbones. After RL training, the Acc0.01 of Qwen3-Coder-30B rose from 32.30% to 40.92%.
• Limits: The authors state that the main experiments used only text-only models, leaving plot-based analysis for future work, and that performance still drops sharply on noisy data even though SR-Scientist stays best. Because the agent only receives top equations, it may re-explore equations that did poorly before. With the appendix backbones Qwen3-8B and Qwen3-14B, SR-Scientist before RL scored below LLM-SR, which the authors take as a sign that the model's own ability matters.

Paper links

External research summaries. These are not HDATF publications or measured product results.