LLM-Guided ODE Discovery and Parameter Inference from Small-Cohort Aggregate Data
2026-07-01 • Machine Learning
Machine LearningArtificial Intelligence
AI summaryⓘ
The authors developed AgentODE, a method that helps discover and understand complex biological models even when there is little detailed data, like in rare diseases. Their method uses summaries of data from groups of patients instead of individual data points, which helps protect privacy. AgentODE uses advanced language models to suggest possible equations and then refines the model parameters based on the summary data. They tested this approach on different problems and a rare disease dataset, showing it finds meaningful models when data is limited and noisy. This approach could help study rare diseases where detailed patient data is hard to get.
Ordinary Differential Equations (ODEs)Mechanistic ModelingRare DiseasesPopulation-level Summary StatisticsParameter InferenceLarge Language Models (LLMs)Privacy PreservationData ScarcityModel Structure DiscoveryRecessive Dystrophic Epidermolysis Bullosa (RDEB)
Authors
Hanning Yang, Meropi Karakioulaki, Lennart Purucker, Tim Litwin, Cristina Has, Moritz Hess
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.