Development of a Hybrid Model for the Paracetamol Batch Dissolution in Ethanol Using Universal Differential Equations

Crystallization is a relevant process in the pharmaceutical industry for product purification and particle production. An efficient crystallization is characterized by crystals produced with the desired attributes. Therefore, modeling this process is a key point to achieve this goal. In this sense, the objective of this work is to propose a hybrid model to describe paracetamol dissolution in ethanol. The universal differential equations methodology is considered in the development of this model, using a neural network to predict the dissolution rate combined with the population balance equations to calculate the moments of the crystal size distribution (CSD) and the concentration. The model was developed using experimental batches. The dataset is composed of concentration measurements obtained using attenuated total reflectance-Fourier transform infrared (ATR-FTIR). The objective function of the optimization problem is to minimize the relative absolute difference between the experimental and the predicted concentration. The hybrid model efficiently predicted the concentration compared to the experimental measurements. Furthermore, the hybrid approach made predictions of the moments of the CSD similar to the population balance model proposed by Kim et al. [1], being able to successfully calculate batches not considered in the training dataset. Moreover, the performance of the hybrid model was similar to the phenomenological one based on population balance. Therefore, the universal differential equations approach is presented as an efficient methodology for modeling crystallization processes with limited information.