Integrating Expert ODEs into Neural ODEs: Pharmacology and Disease Progression

Modeling a system's temporal behaviour in reaction to external stimuli is a fundamental problem in many areas. Pure Machine Learning (ML) approaches often fail in the small sample regime and cannot provide actionable insights beyond predictions. A promising modification has been to incorporate expert domain knowledge into ML models. The application we consider is predicting the patient health status and disease progression over time, where a wealth of domain knowledge is available from pharmacology. Pharmacological models describe the dynamics of carefully-chosen medically meaningful variables in terms of systems of Ordinary Differential Equations (ODEs).