Population Balance Model-Based Hybrid Neural Network for a Pharmaceutical Milling Process

Abstract

Population balances are generally used to predict the particle size distribution resulting from the processing of a particulate material in a milling unit. The key component of such a model is the breakage function. In this work we present an approach to model breakage functions that has utility for situations in which determination of the breakage function from first principles is difficult. Traditionally, heuristic models have been used in those situations but the unstructured nature of such models limits their applicability and reliability. To address this gap, we propose a semi-empirical hybrid model that integrates first principles knowledge with a data-driven methodology that takes into account the material properties, mill characteristics, and operating conditions. The hybrid model combines a discrete form of population balance model with a neural network model that predicts the milled particle size distribution given material and mill information. We demonstrate the usefulness of this approach for compacted API ribbons milled in a lab scale Quadra conical mill for different materials and mill conditions. Comparisons are also given to the predictions obtained via a purely neural network model and a population balance model with a linear breakage kernel.