# LLM-Guided ODE Discovery and Parameter Inference from Small-Cohort Aggregate Data

arXiv: https://arxiv.org/abs/2607.00733 · HTML: https://mlsanity.com/paper/2607.00733/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 42 references that are in the map.
- First posted on arXiv 1 Jul 2026.

## Builds on (most cited first, 19 of 19)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Plan-and-Solve Prompting: Improving Zero-Shot Chain-of-Thought Reasoning by Large Language Models](https://mlsanity.com/paper/2305.04091/) (2023)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Meta-Harness: End-to-End Optimization of Model Harnesses](https://mlsanity.com/paper/2603.28052/) (2026)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Automatic Posterior Transformation for Likelihood-Free Inference](https://mlsanity.com/paper/1905.07488/) (2019)
- [LLM-SR: Scientific Equation Discovery via Programming with Large Language Models](https://mlsanity.com/paper/2404.18400/) (2024)
- [Interpretable Scientific Discovery with Symbolic Regression: A Review](https://mlsanity.com/paper/2211.10873/) (2022)
- [Symbolic Regression with a Learned Concept Library](https://mlsanity.com/paper/2409.09359/) (2024)
- [Highly comparative feature-based time-series classification](https://mlsanity.com/paper/1401.3531/) (2014)
- [Feature-based time-series analysis](https://mlsanity.com/paper/1709.08055/) (2017)
- [Think like a Scientist: Physics-guided LLM Agent for Equation Discovery](https://mlsanity.com/paper/2602.12259/) (2026)
- [LLM4ED: Large Language Models for Automatic Equation Discovery](https://mlsanity.com/paper/2405.07761/) (2024)
- [LLM-ODE: Data-driven Discovery of Dynamical Systems with Large Language Models](https://mlsanity.com/paper/2603.20910/) (2026)

## Abstract (arXiv)

Mechanistic modeling via ordinary differential equations (ODEs) provides interpretable descriptions of complex dynamics and enables inference of underlying mechanisms, which is particularly valuable in clinical settings. However, in rare diseases, both the structure and parameters of the model are typically unknown, while individual-level data is scarce, noisy, heterogeneous, and subject to privacy constraints. In such settings, population-level summary statistics provide a practical privacy-preserving data representation, while capturing heterogeneity further requires modeling parameters as distributions rather than fixed values. Yet no existing method jointly discovers ODE structure and refines parameter distributions solely from summary statistics. We present AgentODE, an end-to-end framework that addresses this gap. An LLM proposes candidate ODE structures, while a tool-augmented inference agent iteratively refines parameter distributions through a diagnosis--update loop, operating on population-level summary statistics alone. We evaluate AgentODE on three benchmark problems across different fields and two clinical datasets, including the rare disease recessive dystrophic epidermolysis bullosa (RDEB), with only 231 observations across 46 patients. AgentODE recovers functionally consistent ODE structures across all settings, and experiments on RDEB demonstrates that in sparse and noisy data settings reasoning from summary statistics promotes mechanistically principled structure discovery, whereas baselines with individual-level data access recover implausible structures despite better predictive performance. AgentODE opens new possibilities for mechanistic modeling of rare diseases directly from population-level summary statistics, where data scarcity and privacy constraints have traditionally limited such analyses.