LLMs Guide ODE Discovery for Rare Diseases from Aggregate Data

Mechanistic modeling using ordinary differential equations (ODEs) is invaluable for understanding complex dynamics, particularly in clinical settings where interpretable descriptions are crucial. However, rare diseases present unique challenges: both the model structure and parameters are often unknown, and individual-level data is scarce, noisy, and subject to privacy concerns. Population-level summary statistics offer a practical, privacy-preserving alternative, but existing methods struggle to jointly discover ODE structure and refine parameter distributions solely from such aggregate data. To address this gap, researchers introduce AgentODE, an end-to-end framework. AgentODE employs a large language model (LLM) to propose candidate ODE structures. A separate, tool-augmented inference agent then iteratively refines parameter distributions through a diagnosis-update loop, operating exclusively on population-level summary statistics. This approach allows for modeling parameters as distributions rather than fixed values, capturing inherent heterogeneity. Evaluations on three benchmark problems and two clinical datasets, including the rare disease recessive dystrophic epidermolysis bullosa (RDEB) with very limited patient data, demonstrate AgentODE's effectiveness. It consistently recovers functionally sound ODE structures across all settings. Notably, for sparse and noisy data like RDEB, reasoning from summary statistics led to mechanistically principled structure discovery, outperforming baselines that, despite having access to individual-level data, yielded implausible structures. AgentODE opens new avenues for mechanistic modeling in data-scarce and privacy-sensitive contexts.