Pediatric patients are at elevated risk of adverse drug reactions, and there is insufficient information on drug safety in children. Complicating risk assessment in children, there are numerous age-dependent changes in the absorption, distribution, metabolism, and elimination of drugs. A key contributor to age-dependent drug toxicity risk is the ontogeny of drug metabolism enzymes, the changes in both abundance and type throughout development from the fetal period through adulthood. Critically, these changes affect not only the overall clearance of drugs but also exposure to individual metabolites. In this study, we introduce time-embedding neural networks in order to model population-level variation in metabolism enzyme expression as a function of age. We use a time-embedding network to model the ontogeny of 23 drug metabolism enzymes. The time-embedding network recapitulates known demographic factors impacting 3A5 expression. The time-embedding network also effectively models the nonlinear dynamics of 2D6 expression, enabling a better fit to clinical data than prior work. In contrast, a standard neural network fails to model these features of 3A5 and 2D6 expression. Finally, we combine the time-embedding model of ontogeny with additional information to estimate age-dependent changes in reactive metabolite exposure. This simple approach identifies age-dependent changes in exposure to valproic acid and dextromethorphan metabolites and suggests potential mechanisms of valproic acid toxicity. This approach may help researchers evaluate the risk of drug toxicity in pediatric populations.