Uncertainty-aware physics-informed meta-learning for predicting niosomal particle size across formulations and...

Accurate prediction of niosomal particle size across diverse formulation compositions and processing conditions remains challenging because experimental datasets are typically limited and heterogeneous. This study presents an uncertainty-aware physics-guided meta-learning (PGML) framework for predicting the mean particle size of niosomal formulations prepared using the thin-film hydration (TFH) method. The framework integrates molecular descriptors, formulation variables, and processing conditions within a shared meta-learning representation, while soft formulation-guided regularization is used to discourage physically implausible model behavior. A probabilistic Gaussian-process prediction component provides predictive uncertainty together with particle-size estimates. The framework was evaluated using 114 formulations collected from 17 published studies and an independent test partition. The final model achieved an RMSE of approximately 0.65, an MAE of 0.43, and an R² of approximately 0.90, while the 95% prediction interval coverage probability (PICP@95%) was approximately 0.90. The results indicate that combining soft physics-guided regularization, task-based learning, and probabilistic prediction can provide accurate particle-size estimates together with information regarding predictive confidence. The proposed framework is intended as a formulation-level decision-support approach for screening and prioritizing experimental conditions when available data are limited and heterogeneous.