Descriptor-Guided Model-Zoo Learning of Nonlinear Quality Attributes in Daidzein-Loaded Hydroxyapatite Nanoparticles

Abstract Daidzein-loaded hydroxyapatite nanoparticles are promising carrier systems for improving the formulation performance of poorly soluble bioactive compounds; however, their critical quality attributes may show nonlinear and response-specific behaviour that is not always fully captured by conventional response surface modelling. This study implemented a descriptor-guided model-zoo learning framework to reanalyse a 17-run Quality by Design dataset of daidzein-loaded hydroxyapatite nanoparticles. Sixteen formulation-derived descriptors were generated from hydroxyapatite-to-daidzein ratio, dispersion volume and loading time, including quadratic, interaction, logarithmic, square-root and ratio-based terms. Descriptor-subset screening was then performed across multiple regression algorithms for response-wise prediction of particle size, entrapment efficiency and zeta potential. The reconstructed QbD/RSM model was most suitable for particle size, achieving internal leave-one-out cross-validation R² of 0.965 and RMSE of 0.725 nm. For entrapment efficiency, descriptor-guided Gaussian Process regression using loading time, squared carrier ratio and carrier-to-volume ratio improved prediction compared with QbD/RSM, giving LOOCV R² of 0.473. Descriptor Elastic Net using squared loading time, log-transformed dispersion volume, squared carrier ratio and carrier-to-volume ratio was selected for zeta potential, achieving LOOCV R² of 0.381 and low optimized-checkpoint error. Explainable AI analysis using permutation importance, SHAP and LIME identified response-specific descriptor contributions, while Lasso-based surrogate equations and symbolic regression provided interpretable equation-based approximations. These findings show that descriptor-guided model-zoo learning can extract additional predictive and interpretative value from small QbD formulation datasets while preserving formulation relevance and response-wise interpretability.