  Traditional models of glucose-insulin dynamics rely on heuristic
parameterizations chosen to fit observations within a laboratory setting.
However, these models cannot describe glucose dynamics in daily life. One
source of failure is in their descriptions of glucose absorption rates after
meal events. A meal's macronutritional content has nuanced effects on the
absorption profile, which is difficult to model mechanistically. In this paper,
we propose to learn the effects of macronutrition content from glucose-insulin
data and meal covariates. Given macronutrition information and meal times, we
use a neural network to predict an individual's glucose absorption rate. We use
this neural rate function as the control function in a differential equation of
glucose dynamics, enabling end-to-end training. On simulated data, our approach
is able to closely approximate true absorption rates, resulting in better
forecast than heuristic parameterizations, despite only observing glucose,
insulin, and macronutritional information. Our work readily generalizes to meal
events with higher-dimensional covariates, such as images, setting the stage
for glucose dynamics models that are personalized to each individual's daily
life.
