SR-Scientist: Scientific Equation Discovery With Agentic AI (2510.11661v1)

Abstract: Recently, 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.

• The paper improves symbolic regression by integrating agentic AI and reinforcement learning to autonomously discover and refine scientific equations.
• It employs a dual-tool framework combining data analysis and equation evaluation to optimize constants and support long-horizon optimization.
• Results show 6–35% performance gains with robust generalization under noise and out-of-domain scenarios across multiple scientific domains.

SR-Scientist: Agentic AI for Scientific Equation Discovery

SR-Scientist presents a comprehensive framework for symbolic regression (SR) that leverages agentic capabilities of LLMs to autonomously discover scientific equations. The system advances the state-of-the-art by integrating code interpreters as tools, enabling long-horizon optimization, and employing reinforcement learning (RL) for agent self-improvement. This essay provides a technical analysis of the framework, its empirical results, and its implications for AI-driven scientific discovery.

Framework Architecture and Agentic Workflow

SR-Scientist redefines the role of LLMs in SR from passive equation proposers to autonomous agents capable of iterative hypothesis generation, data analysis, and equation refinement. The agent operates within a ReAct-style framework, interleaving reasoning steps with tool calls for data analysis and equation evaluation. The code interpreter is wrapped into two primary tools: a data analyzer ($T_1$) and an equation evaluator ($T_2$). $T_1$ enables statistical and exploratory analysis of the input data, while $T_2$ accepts equation skeletons and optimizes their constants using the BFGS algorithm, reporting metrics such as MSE, NMSE, and MAPE.

Figure 1: The inference framework of SR-Scientist, illustrating autonomous long-horizon optimization via code interpreters and an experience buffer for context management.

To address context length limitations inherent in current LLMs, SR-Scientist implements an experience buffer that stores previously explored equations and their scores. At each iteration, the agent fetches top-performing equations from the buffer as in-context exemplars, facilitating continual optimization and bypassing context constraints.

Training and Reinforcement Learning Pipeline

The training pipeline synthesizes diverse scientific scenarios across four domains (chemistry, biology, physics, material science) using a hybrid rule-based and model-based approach. Equation skeletons are generated and instantiated with physically meaningful constants, followed by data generation via grid sampling or ODE solvers. The RL framework utilizes a log-linear reward function based on MAPE, providing continuous feedback and mitigating reward sparsity. Policy optimization is performed using Group Relative Policy Optimization (GRPO), with batch-level asynchronous rollouts and no KL penalty to encourage exploration.

Empirical Evaluation and Results

SR-Scientist is evaluated on the LSR-Synth benchmark, which is specifically designed to prevent equation memorization by LLMs. The main metric is accuracy-to-tolerance ($\text{Acc}_\tau$), which robustly aggregates performance across problems and domains. SR-Scientist consistently outperforms both traditional and LLM-based baselines, with absolute margins of 6–35% depending on the backbone model.

Figure 2: Detailed results of in-domain (ID) and out-of-domain (OOD) performance using $\text{Acc}_{0.01}$ across scientific domains.

Notably, with GPT-OSS-120B as the backbone, SR-Scientist achieves $\text{Acc}_{0.01}=63.57\%$ and $\text{Acc}_{0.001}=49.35\%$, surpassing all baselines. RL training further improves performance, especially for smaller models such as Qwen3-Coder-30B, demonstrating the agent's capacity for self-evolution.

Robustness, Generalization, and Symbolic Accuracy

SR-Scientist exhibits strong robustness to noise, maintaining superior performance as Gaussian noise is injected into the training data.

Figure 3: Noise robustness analysis for Qwen, GLM, and GPT backbones.

The framework also generalizes well to OOD data, with performance gains observed in material science and stable results across other domains. Symbolic accuracy, measured by equivalence to ground truth equations, is highest for SR-Scientist among all tested methods.

Figure 4: Equations discovered for PO10 and PO37 physics problems, highlighting structural and constant accuracy.

Ablation and Behavioral Analysis

Ablation studies confirm the critical role of the data analyzer tool and the experience buffer. Removing either component leads to substantial drops in accuracy, especially for larger LLMs.

Figure 5: Overall performance under different maximum turns, demonstrating the impact of long-horizon optimization.

Tool call analysis reveals that most agent actions are dedicated to equation evaluation, with a significant fraction allocated to data statistics and residual error analysis. RL training increases the agent's sophistication in data analysis, particularly for smaller models.

Figure 6: The tool call behaviors of different models, showing distribution across analysis types.

Computational Considerations and Cost

SR-Scientist is computationally efficient, with API costs for GPT-OSS-120B estimated at \$0.25 per problem and wall-clock times under 5 hours for batch inference on 129 problems using two NVIDIA H100s. The framework is scalable and practical for real-world scientific applications.

Implications and Future Directions

SR-Scientist demonstrates that agentic LLMs, when equipped with tool-use and RL-driven self-improvement, can autonomously discover interpretable scientific equations with high precision, robustness, and generalization. The framework's minimal reliance on human-defined pipelines and its capacity for long-horizon optimization mark a significant step toward fully autonomous scientific discovery systems.

Theoretical implications include the feasibility of end-to-end agentic SR pipelines and the utility of continuous reward functions for symbolic tasks. Practically, SR-Scientist can be extended to more complex domains, integrated with simulation environments, or adapted for multi-agent scientific collaboration. Future work may explore scaling to larger models, more diverse toolsets, and integration with experimental data streams.

Conclusion

SR-Scientist advances symbolic regression by transforming LLMs into autonomous scientific agents capable of iterative hypothesis generation, data analysis, and equation refinement. The framework achieves state-of-the-art results in precision, generalization, and symbolic accuracy, and demonstrates robust performance under noise and OOD conditions. Its agentic architecture and RL pipeline provide a blueprint for future AI systems in scientific discovery.