PILL-CoDe: Inverse design of polypills via automatic differentiation for prescribed drug-release kinetics

Polypills are single oral dosage forms that combine multiple active pharmaceutical ingredients and excipients, enabling fixed-dose combination therapies, coordinated multi-phase release, and precise customization of patient-specific treatment protocols. Recent advances in additive manufacturing facilitate the physical realization of multi-material excipients, offering superior customization of target release profiles. However, polypill formulations remain tuned by ad hoc parameter sweeps. The current design workflows are ill-suited for the systematic exploration of the high-dimensional space of shapes, compositions, and release behaviors. We present PILL-CoDe, a polypill co-design framework that simultaneously optimizes tablet geometry and excipient distribution to match prescribed drug-release kinetics. The framework couples a supershape parametrization of the pill geometry with a coordinate-based neural network representation of the excipient distribution, and governs dissolution through a coupled system of modified Allen-Cahn and Fickian diffusion equations. Implemented in JAX, the entire pipeline is end-to-end differentiable, with automatic differentiation providing exact sensitivities for gradient-based co-optimization of shape and composition under manufacturability constraints. We demonstrate the method through single-phase and multi-excipient case studies, showing accurate matching of both monotonic and non-monotonic target release profiles.