Keynote #2: Toward Agentic AI Systems for Interpretable Scientific Equation Discovery

Equation discovery is a crucial aspect of computational scientific discovery, traditionally approached through symbolic regression (SR) methods that focus mainly on data-driven equation search. Current approaches often struggle to fully leverage the rich domain-specific knowledge that scientists typically rely on. We present LLM-SR, an agentic AI-based iterative approach that combines the power of large language models (LLMs) with evolutionary program search and data-driven optimization to discover scientific equations more effectively and efficiently while incorporating scientific prior knowledge. LLM-SR integrates several key aspects of the agentic scientific discovery pipeline, namely, scientific knowledge representation and reasoning (enabled through autonomous LLM agents using prompting and prior knowledge), hypothesis generation (via agent-driven equation skeleton proposals), data-driven evaluation and optimization, and evolutionary search for iterative refinement. Through this integration, our approach discovers interpretable and physically meaningful equations while ensuring efficient exploration of the equation search space and generalization to out-of-domain data. We will demonstrate LLM-SR’s effectiveness across various scientific domains—nonlinear oscillators, bacterial growth, and material stress behavior. This work not only improves the accuracy and interpretability of discovered equations but also enhances the autonomy and efficiency of the equation discovery process, aligning with the goals of agentic AI systems for accelerating scientific innovation.