SR-Scientist: Scientific Equation Discovery With Agentic AI¶

🕒 Published (v1): 2026-01-01 · Source: ICLR · Venue: ICLR 2026 · link

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Agentic AI for scientific equation discovery with active hypothesis and verification loop

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TL;DR¶

SR-Scientist upgrades the LLM's role in symbolic regression from a passive equation proposer inside genetic programming to a fully autonomous agent that writes code, analyzes data, evaluates equations, and self-optimizes over long horizons. It outperforms prior LLM-based SR methods by 6–35 percentage points across four scientific disciplines. An end-to-end GRPO reinforcement learning pipeline further boosts the agent's performance without task-specific human engineering.

Problem¶

Existing LLM-assisted symbolic regression (SR) systems slot the LLM into a fixed human-crafted pipeline—typically as an equation generator inside genetic programming—denying it the ability to inspect data, form iterative hypotheses, or adaptively decide its own workflow. This passive role fails to exploit LLMs' emergent capacity for autonomous, multi-step scientific reasoning.

Method¶

SR-Scientist wraps a code interpreter into two tools: a data analyzer ($T_1$) for arbitrary exploratory code (statistics, residual analysis, etc.) and an equation evaluator ($T_2$) that accepts an equation skeleton with constant placeholders and runs BFGS to fit constants, returning MAPE. The LLM agent operates in a ReAct loop—reasoning, tool-calling, observing—for up to $M = 25$ turns per iteration over $N = 40$ iterations. An experience buffer $E = \{(e_i, s_i)\}$ stores all explored equations ranked by MAPE; each new iteration fetches the top-$K$ equations as in-context priors, bypassing context-length constraints. The optimization goal is set as a MAPE threshold and tightened across iterations. For training, GRPO is applied with a continuous log-linear reward: $$R = \text{clip}\!\left(\frac{\lg s_{\max} - \lg s}{\lg s_{\max} - \lg s_{\text{goal}}},\, 0,\, 1\right)$$ where $s$ is the best equation's MAPE in a rollout; the KL penalty against the reference policy is omitted to encourage exploration. Training data (1024 problems) is synthesized from rule-based and model-based equation skeleton construction.

Key Contributions¶

SR-Scientist framework: autonomous LLM agent for symbolic regression via tool-driven, long-horizon data analysis and equation optimization with minimal human-defined pipeline.
Experience buffer mechanism enabling iterative cross-context knowledge reuse without growing context length.
End-to-end RL pipeline (GRPO with continuous reward) for improving agent capabilities through self-generated rollouts.
Empirical demonstration of robustness to noise, OOD generalization, and symbolic accuracy advantages over GP, deep-learning, and prior LLM-based SR baselines.

Results¶

Overall accuracy: SR-Scientist with GPT-OSS-120B reaches Acc$_{0.01}$ = 63.57%, Acc$_{0.001}$ = 49.35% on LSR-Synth (129 problems across chemistry, biology, physics, material science).
Margin over best LLM baseline (LLM-SR): absolute gains of 6%–35% across the five backbone models tested.
RL training on Qwen3-Coder-30B-A3B raises Acc$_{0.01}$ from 32.30% → 40.92% and Acc$_{0.001}$ from 16.02% → 20.69%.
Symbolic accuracy: SR-Scientist (best) = 7.75% vs. PySR = 4.65% and LLM-SR = 5.43%.
Noise robustness: consistently best across Gaussian noise $\sigma \in \{0.01, 0.05, 0.1\}$.
Ablation: removing $T_1$ (data analyzer) drops GPT backbone from 63.57% → 35.66% Acc$_{0.01}$; removing experience buffer drops it to 57.36%.
Turn-length effect: performance improves significantly from 10 → 25 turns per iteration; gains plateau beyond 25 turns.

Limitations¶

RL training demonstrated only on Qwen3-Coder-30B-A3B due to compute/infrastructure constraints; cross-model RL results are relegated to appendix.
Uses text-only LLM backbone; cannot natively process plots generated during data analysis (code is prompted to avoid figure output).
Inference is compute-intensive (up to 1,000 LLM calls per problem); practical deployment cost is discussed but not fully resolved.
Evaluation restricted to LSR-Synth; real-world scientific datasets with ground-truth equations may present different challenges.
Symbolic accuracy remains low even for the best method (~7.75%), suggesting exact structure recovery is still far from solved.

Relevance to Agentic AI / LLM Agents¶

SR-Scientist is a concrete instantiation of the agentic paradigm—minimal human-designed pipeline, goal-directed long-horizon tool use, and closed-loop feedback—applied to a hard NP-complete scientific search problem, demonstrating that agentic design choices (tool composition, experience buffers, turn depth) matter more than backbone scale alone. The experience buffer pattern is a transferable technique for any agent facing context-length ceilings during iterative optimization tasks. The end-to-end GRPO training without a KL penalty is noteworthy for agentic RL: it suggests that reference-model constraints may suppress the exploration necessary for open-ended scientific search. This work expands the empirical case for agentic LLMs beyond software engineering and GUI tasks into quantitative scientific discovery, with reproducible benchmarks on LSR-Synth.