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

arXiv: https://arxiv.org/abs/2607.13608 · HTML: https://mlsanity.com/paper/2607.13608/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Web, search, and research agents, one of 16 directions in LLM agents and tool use.
- Builds on 21 of its 61 references that are in the map.
- First posted on arXiv 15 Jul 2026.

## Placed in

- LLM agents and tool use / [Web, search, and research agents](https://mlsanity.com/agents/web-search-and-research-agents/)

## Builds on (most cited first, 21 of 21)

- [The AI Scientist: Towards Fully Automated Open-Ended Scientific Discovery](https://mlsanity.com/paper/2408.06292/) (2024)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Agent Laboratory: Using LLM Agents as Research Assistants](https://mlsanity.com/paper/2501.04227/) (2025)
- [Automated Design of Agentic Systems](https://mlsanity.com/paper/2408.08435/) (2024)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Towards End-to-End Automation of AI Research](https://mlsanity.com/paper/2606.15497/) (2026)
- [Interpretable Scientific Discovery with Symbolic Regression: A Review](https://mlsanity.com/paper/2211.10873/) (2022)
- [OMNI-EPIC: Open-endedness via Models of human Notions of Interestingness with Environments Programmed in Code](https://mlsanity.com/paper/2405.15568/) (2024)
- [LLM-SRBench: A New Benchmark for Scientific Equation Discovery with Large Language Models](https://mlsanity.com/paper/2504.10415/) (2025)
- [Probabilistic Grammars for Equation Discovery](https://mlsanity.com/paper/2012.00428/) (2020)
- [A computational framework for physics-informed symbolic regression with straightforward integration of domain knowledge](https://mlsanity.com/paper/2209.06257/) (2022)
- [Shape-constrained Symbolic Regression -- Improving Extrapolation with Prior Knowledge](https://mlsanity.com/paper/2103.15624/) (2021)
- [When AI Co-Scientists Fail: SPOT-a Benchmark for Automated Verification of Scientific Research](https://mlsanity.com/paper/2505.11855/) (2025)
- [Automated Scientific Discovery: From Equation Discovery to Autonomous Discovery Systems](https://mlsanity.com/paper/2305.02251/) (2023)
- [Symbolic Regression by Exhaustive Search: Reducing the Search Space Using Syntactical Constraints and Efficient Semantic Structure Deduplication](https://mlsanity.com/paper/2109.13895/) (2021)
- [PaperOrchestra: A Multi-Agent Framework for Automated AI Research Paper Writing](https://mlsanity.com/paper/2604.05018/) (2026)
- [Multiple Choice Questions: Reasoning Makes Large Language Models (LLMs) More Self-Confident, Especially When They are Wrong](https://mlsanity.com/paper/2501.09775/) (2025)
- [Knowledge Integration for Physics-informed Symbolic Regression Using Pre-trained Large Language Models](https://mlsanity.com/paper/2509.03036/) (2025)
- [MDBench: Benchmarking Data-Driven Methods for Model Discovery](https://mlsanity.com/paper/2509.20529/) (2025)
- [Incorporating Background Knowledge in Symbolic Regression using a Computer Algebra System](https://mlsanity.com/paper/2301.11919/) (2023)
- [Discovering equations from data: symbolic regression in dynamical systems](https://mlsanity.com/paper/2508.20257/) (2025)

## Abstract (arXiv)

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.