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

Jul 16, 2026

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Mechanistic modeling via ordinary differential equations (ODEs) enables interpretable descriptions of complex dynamics and supports inference of underlying mechanisms, especially in clinical settings. For rare diseases, model structure and parameters are usually unknown and individual-level data are scarce, noisy, heterogeneous, and privacy constrained. Population-level summary statistics offer privacy-preserving representation, but heterogeneity requires treating parameters as distributions. No existing method jointly discovers ODE structure and learns parameter distributions solely from summaries, which motivates AgentODE.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages38

Reading Time1 h 36 min

Abstract

Introduction

Challenges in rare-disease ODE modeling

Existing ODE discovery and mixed-effects approaches

Motivation for agentic LLM-based structure discovery

Proposed framework: AgentODE

arXiv :2607 .00733v 1 [ cs .LG] 1 Jul 2026 LLM-Guided ODE Discovery and Parameter Inference from Small-Cohort Aggregate Data Hanning Yang 1∗ , Meropi Karakioulaki2 , Lennart Purucker3 , Tim Litwin 1 , Cristina Has2 , Moritz Hess 1 1Institute of Medical Biometry and Statistics, Faculty of Medicine and Medical Center, University of Freiburg, Germany 2Department of Dermatology, Medical Faculty and Medical Center, University of Freiburg, Germany 3Prior Labs, University of Freiburg, Germany [hanning.yang@uniklinik-freiburg.de](hanning.yang@uniklinik-freiburg.de) Abstract 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 1. 1 Introduction Mechanistic models based on ordinary differential equations (ODEs) provide a principled framework for describing the dynamics of complex systems across domains such as biology, medicine, and engineering[Raue et al., 2013] . By explicitly encoding mechanistic relationships between variables, ODE models offer interpretability, support reasoning about underlying processes, and enable extrapolation beyond observed data. These properties make ODEs particularly valuable in clinical settings, where understanding disease mechanisms is critical. However, constructing ODE models typically requires substantial expert knowledge to specify both the functional structure and parameters of the system. In rare diseases, such knowledge is often limited, while available data are typically scarce, noisy, heterogeneous, and subject to privacy constraints [Hilgers et al., 2016] . Capturing this heterogeneity requires modeling parameters as distributions rather than fixed values [Jaqaman and Danuser, 2006] . These challenges make reliable 1 Code available at [https://github.com/HanningYang/AgentODE](https://github.com/HanningYang/AgentODE). Preprint. model identification difficult in practice, even for approaches that rely on fitting individual-level data. In practice, population-level summary statistics are often used as a pragmatic alternative, as they enable privacy-preserving data sharing and can still provide an informative representation under noise, irregular sampling, and small cohort sizes. While automatic structur

FAQs

What problem does AgentODE address in rare-disease modeling?

AgentODE targets the gap where ODE structure and parameter distributions must be learned jointly from population-level summary statistics when individual-level data are scarce, noisy, heterogeneous, and privacy constrained.

How does AgentODE use LLMs during ODE discovery?

An LLM proposes candidate ODE structures, and an inference agent then iteratively refines parameter distributions using a diagnosis–update loop operating only on population-level summary statistics.

How is AgentODE evaluated, and what does it achieve on sparse clinical data?

The framework is evaluated on benchmark problems and two clinical datasets, including RDEB with 231 observations across 46 patients. It recovers functionally consistent ODE structures, and reasoning from summaries helps structure discovery in sparse, noisy settings where baselines using individual-level data can yield implausible structures.

Jul 16, 2026

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