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

2026-07-15

AI Summary

This work addresses the challenge of automatically discovering biologically plausible ordinary differential equation (ODE) models from data, moving beyond purely black-box fitting approaches. The authors propose MEDA, a novel system that, for the first time, integrates knowledge-guided mechanistic constraints and formal biological knowledge into a large language model (LLM)-driven ODE discovery pipeline. By synergistically combining symbolic regression, an agent-based framework, background knowledge retrieval, and numerical fitting, MEDA enables interpretable modeling of biological dynamical systems. Experimental results demonstrate that MEDA accurately recovers both state variables and ODE structures across diverse tasks—including reproducing established models, extrapolating to unseen variants, and performing open-ended discovery—while generating novel models that are not only mathematically consistent but also biologically credible.

Abstract

Automatic scientific discovery has long been a goal of computational scholars - a machine that can discover nature's secrets on its own, moving computational systems beyond data-fitting tools toward the generation and refinement of mechanistic models of the universe. Recent advances in symbolic regression (SR) and large-language-model (LLM)-based agents suggest that such systems can recover equations from data, incorporate domain priors, and automate parts of the research workflow. However, most existing approaches either focus on narrow equation-discovery benchmarks or broad end-to-end automation pipelines, while biological systems remain comparatively underexplored. Here, we introduce the MEDA system, an LLM- and SR-powered agentic framework for discovering ordinary-differential-equation (ODE) models of biological and biologically inspired dynamical systems. MEDA retrieves background knowledge, defines admissible variables, generates mechanistic constraints, proposes candidate ODEs, and fits and evaluates them. We evaluate it across canonical model retrieval, reasoning-based extrapolation to unseen variants, and open-ended discovery, with and without experimental data. Across these settings, MEDA recovered the correct state variables, achieved strong structural recovery in retrieval and extrapolation tasks, and produced biologically plausible discovery-oriented models. Ablation and robustness analyses show that knowledge-guided formalization and mechanistic constraints are load-bearing components, whereas numerical fitting alone can preserve trajectory-compatible but biologically incorrect equations.

Problem

• ordinary differential equations
• biological systems
• automatic discovery
• mechanistic modeling
• symbolic regression

Innovation

• large language model
• symbolic regression
• ODE discovery
• agentic system
• biological modeling