  Diabetes encompasses a complex landscape of glycemic control that varies
widely among individuals. However, current methods do not faithfully capture
this variability at the meal level. On the one hand, expert-crafted features
lack the flexibility of data-driven methods; on the other hand, learned
representations tend to be uninterpretable which hampers clinical adoption. In
this paper, we propose a hybrid variational autoencoder to learn interpretable
representations of CGM and meal data. Our method grounds the latent space to
the inputs of a mechanistic differential equation, producing embeddings that
reflect physiological quantities, such as insulin sensitivity, glucose
effectiveness, and basal glucose levels. Moreover, we introduce a novel method
to infer the glucose appearance rate, making the mechanistic model robust to
unreliable meal logs. On a dataset of CGM and self-reported meals from
individuals with type-2 diabetes and pre-diabetes, our unsupervised
representation discovers a separation between individuals proportional to their
disease severity. Our embeddings produce clusters that are up to 4x better than
naive, expert, black-box, and pure mechanistic features. Our method provides a
nuanced, yet interpretable, embedding space to compare glycemic control within
and across individuals, directly learnable from in-the-wild data.
