A structure-preserving hybrid learning framework for compartmental pharmacokinetic models.

Pharmacokinetic (PK) models are widely used in drug development and dose planning, but they often face a trade-off between interpretability and flexibility. Traditional physiology-based PK models are transparent but may be too simple to capture complex or nonlinear behavior, while AI models are more flexible but can violate basic physical constraints such as nonnegativity or mass balance. In this work, we propose a constrained hybrid AI-PK approach in which small AI components are embedded within the PK equations as bounded corrections to mechanistic rates. The correction network is constructed to be internally conservative across compartments and to act as a controlled perturbation of the base model. We provide a simple mathematical analysis showing that this design preserves key qualitative properties, including boundedness and, under suitable conditions, positivity and stability. Numerical experiments on simulated and reported PK datasets show that the constrained hybrid model improves prediction accuracy and yields more stable extrapolation than both purely mechanistic and unconstrained hybrid models, while respecting the underlying physical structure.