Crystallization is one of the most common processes used for purification and product design in the pharmaceutical industry, where controlling crystal characteristics is critical for maintaining stable product quality and operational efficiency. While neural networks have been proven to improve control in these systems (Ceorgieva and De Azevedo, 2006; Paengjuntuek et al., 2012; Kittisupakorn et al., 2017; Nielsen, 2020; Zheng et al., 2022; Wu et al., 2023; Moraes et al., 2023; Lima et al., 2024), their purely data-driven nature can limit transferability when the experimental setup changes. In contrast, physics-based models such as population balance models offer excellent transferability but are difficult to accurately parameterize (Kim et al., 2023). In this work, we develop a physics-informed machine learning framework that combines the strengths of both approaches to model crystallization systems. Our approach integrates the population balance model – considering nucleation, growth, and dissolution of crystals – into the neural network structure through the method of moments, ensuring that predictions are consistent with both the training data and the underlying physics. In addition, real-time sensor data from ReactIR and FBRM are incorporated into the training dataset and used for experimental validation. Using paracetamol in ethanol as a case study, the developed model is validated by its ability to backtrack parameter values in the population balance model and accurately predict experimental results under varying setups. This physics-informed framework offers insight into the tradeoffs between data-driven and model-based predictions in crystallization and shows a promising pathway for possible implementation in real-world process controls.
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