Hybrid Semi-mechanistic and Machine Learning Solubility Regression Modeling for Crystallization Process Development

Abstract

Solubility regression modeling is foundational for several chemical engineering applications, particularly for crystallization process development. Traditionally, these models rely on parametric semimechanistic approaches such as the Van’t Hoff Jouyban-Acree (VH-JA) cosolvency model. Although these models generally provide narrow prediction intervals, they can exhibit increased bias when dealing with significant solute heat capacities or complex mixture effects. This study explores machine learning, including Random Forests, Support Vector Machines, Gaussian Process Regression, and Neural Networks, as potential alternatives. While most machine learning models offered a lower training error, it was observed that their predictive quality quickly deteriorates further from the training data. Hence, a hybrid approach was explored to leverage the low bias of machine learning and the low variance of the VH-JA model through heterogeneous locally weighted bagging ensembles. Key to the methodology is quantifying, tracking, and minimizing the uncertainty using the ensemble. This approach was illustrated through a case study on the solubility of ketoconazole in binary mixtures of 2-propanol and water. The optimal hybrid ensemble, comprising of 58% stepwise VH-JA models and 42% machine learning models, reduced the training root-mean-squared error and maximum absolute percentage error by ≈30% compared to the full VH-JA, while preserving a comparable prediction interval.