  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
progression of disease under medications, where a plethora 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). However, these models only describe a limited
collection of variables, and these variables are often not observable in
clinical environments. To close this gap, we propose the latent hybridisation
model (LHM) that integrates a system of expert-designed ODEs with
machine-learned Neural ODEs to fully describe the dynamics of the system and to
link the expert and latent variables to observable quantities. We evaluated LHM
on synthetic data as well as real-world intensive care data of COVID-19
patients. LHM consistently outperforms previous works, especially when few
training samples are available such as at the beginning of the pandemic.
