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Crystallization is a crucial process in the pharmaceutical industry, usually modeled by Population Balance Models (PBM). This study introduces a novel approach, combining PBM with machine learning techniques, specifically the Universal Differential Equation (UDE), to describe a batch cooling crystallization process. Unlike conventional methods, UDE eliminates the need for defining a supersaturation term and was applied to model the nucleation, growth, and dissolution of potassium sulfate in water. In this study, three UDE models for supersaturated condition and one for undersaturated condition were developed, aiming to predict particle count, length, surface area, volume, and concentration. Initially, these models were trained using all available experimental data from a previous study for the potassium sulfate batch crystallization. They were validated with simulated data generated by the PBM. In a second scenario, the models were trained with a subset of the experimental data and tested with the remainder. The UDE models performed efficiently, exhibiting similar mean squared error and mean absolute error compared to conventional PBMs. Notably, the UDE approach demonstrated an advantage in requiring a smaller training dataset. This innovative coupling of UDE and PBM offers a less complex yet effective model to capture essential aspects of crystallization kinetics and variables' dynamics. Particularly, UDE models excel in predicting nucleation kinetics, making them a valuable alternative to conventional representations. Furthermore, this approach can be easily adapted to various crystallization processes involving different phenomena, enhancing its versatility and potential impact. [Display omitted] • A crystallization process was modeled using Universal Differential Equations (UDE). • The UDE was efficiently developed using only experimental data. • The UDE does not need the definition of a supersaturation term. [ABSTRACT FROM AUTHOR]

• A new approach for multi-objective optimization of Pressure Swing Adsorption. • Fisher–Snedecor test to the solution of a multi-objective problem is deduced. • The concept of Feasible Operating Regions is presented to address the study case. • The obtained Pareto region is divided into operating sub-regions clustering. Optimization of cyclic adsorption processes is a challenging issue due to the dynamic-operating complexity of these processes. In this context, this work proposes a new approach for multi-objective optimization of Pressure Swing Adsorption (PSA) units, extending the concept of the Pareto front to Pareto region. The proposed methodology, hitherto unexplored in the literature, consists of integrating a likelihood test, an arrangement from the Fisher–Snedecor test to the solution of a multi-objective problem provided by a Swarm Particle Optimization technique. The Pareto region is divided into operating sub-regions that meet the optimization constraints and prioritize a determined objective by a clustering process. These sub-regions make the operation more flexible. Furthermore, the analysis of the operating variables feasible operation interval demonstrated to be an important tool to provide information regarding the system behavior. As a study case, it is presented the optimization of a PSA process for syngas purification. The results demonstrate that the methodology proposed here uses the feasible operation region map and the clustering strategy to exploit the multi-objective optimization. Therefore, providing a more reliable and precise optimization of PSA units, while providing an important tool for making decisions in the PSA system. [ABSTRACT FROM AUTHOR]

• Material screening and simultaneous processes optimization. • Deep learning neural networks providing deep insights about the process behavior. • A nested loop is proposed to provide the integration of the level within the optimization framework. • Uncertainty assessment of the optimal points provides a map of the feasible operating regions. The present work proposes a novel strategy for simultaneous material screening and process optimization. This strategy is based on the capacities of deep neural networks to extract knowledge of a database. It makes use of a nested optimization loop which is designed to couple the process and material points of view simultaneously. The optimization problem results are analyzed by a Fisher–Snedecor test, designed to assess the optimal points uncertainties, building the process's feasible operating regions. This methodology describes the processes' possible operating points that lead to optimal conditions, considering the material type as a decision variable. The methodology shows that this complex problem can be better understood when the uncertainties are taken into consideration. On the other hand, the proposed optimization problem can provide a way to address the issues related to optimizing adsorption processes considering the material screening. [ABSTRACT FROM AUTHOR]