Automatic Ordinary Differential Equations Discovery For Biological Systems Using Large Language Model Powered Agentic System

Automatic Scientific Discovery (ASD) aims to move computational tools beyond simple data fitting toward the generation of mechanistic models. The authors introduce the Mechanistic Equation Discovery Agentic (MEDA) system, which leverages Large Language Models (LLMs) and symbolic regression to discover ordinary differential equations (ODEs) for biological systems. Unlike traditional approaches that focus on numerical curve-fitting, MEDA mimics the scientific process by integrating literature-based background knowledge, defining admissible variables, and applying mechanistic constraints to guide the search for symbolic equations.

MEDA operates through a series of specialized, inspectable agents coordinated by an orchestrator. The pipeline includes:

• Literature Surveyor: Gathers background knowledge and qualitative dynamical signatures.
• Formalizer: Translates knowledge into machine-readable constraints and seed equations.
• Runner: Performs a constrained evolutionary search over polynomial ODE systems.
• Reporter/Recapper/Evaluator: Summarizes, critiques, and validates the discovered models against ground truth.

This modular design allows researchers to audit the reasoning behind each discovered equation, ensuring that the final model is not just a black-box predictor but a scientifically defensible hypothesis.

MEDA was evaluated across various biological domains, including epidemiology, population dynamics, and cellular signaling. The results demonstrate that the system reliably identifies correct state variables and mechanistic skeletons. A key finding is that knowledge-guided formalization is a load-bearing component; while numerical data can improve parameter calibration, it can also lead the system toward "overfitted" models that match trajectories but violate biological principles. The system's ability to operate in a "constraint-only" mode—where no time-series data is provided—highlights its utility in scenarios where experimental data is unavailable or unreliable.