Speaker
Description
Biological data often exhibit substantial heterogeneity between individuals. While part of this variability reflects random biological variation, systematic differences may arise from physiological diversity or disease. To reflect this diversity in mechanistic models, we often use the same mathematical equations, while individuals differ in parameter values that govern system dynamics. Capturing this structure, without disregarding the relevant physiological variability remains challenging for regular universal differential equations (UDEs).
In regular UDEs, mechanistic ordinary differential equations are combined with neural networks to learn a single population-level relationship, and therefore struggle to represent systematic heterogeneity between individuals. To address this limitation, we propose conditional universal differential equations (cUDEs). Instead of learning a single function, cUDEs learn a parameterized family of functions conditioned on a latent variable, allowing the model to capture individual differences while preserving a shared mechanistic structure.
We demonstrate this approach by modelling postprandial C-peptide production in a mixed population of healthy individuals and individuals with type 2 diabetes. Combining cUDEs with symbolic regression enables recovery of interpretable mechanistic relationships while accounting for population heterogeneity.
