Abstract
Crystallisation is a promising and scalable alternative to chromatography for biologics purification. However biologics such as proteins and peptides often crystallise only in narrow operating windows, limiting process flexibility. Template-induced crystallisation can lower supersaturation requirements and expand feasible operating ranges, yet the template dependence of nucleation and growth kinetics remains difficult to parametrise mechanistically. To address this, we develop and experimentally validate uncertainty-aware hybrid models for lysozyme crystallisation on hydroxyl- and carboxyl-functionalised silica templates. A mechanistic population-balance model is coupled to a data-driven regressor that maps operating conditions and template variables to effective nucleation and growth rates. We compare a neural network baseline against a structured neural power-law surrogate, which embeds a supersaturation-dependent power-law form. Both hybrid models are trained in-the-loop via differentiable simulation, and variational inference is used to obtain posterior parameter distributions and calibrated predictive uncertainty. Across cross-validation and off-grid tests at previously unseen combinations of temperature and template loading, the hybrid models accurately reproduce solute concentration dynamics and capture key particle-size trends, while the neural power-law surrogate provides improved robustness and faster uncertainty quantification. These results support hybrid, uncertainty-aware PBMs as practical tools for prediction, design-space exploration, and comparison of template-enabled protein crystallisation processes.