Integrating Bayesian Optimization for Enhancing Parameter Estimation Workflows for Modeling Crystallization Processes

Abstract

Accurate estimation of kinetic parameters is essential for developing population balance models in crystallization processes. Parameter estimation (PE) problems are often formulated as black-box optimization tasks, which are computationally expensive due to the large parameter space and the wide variability of crystallization mechanisms across several orders of magnitude. Bayesian optimization (BO) has emerged as a promising approach for efficiently solving such problems with costly objective function evaluations. This work investigates the role of BO in crystallization parameter estimation workflows under both frequentist and Bayesian formulations. First, we assess its effectiveness in improving computational efficiency for the frequentist approach, where parameter estimation is posed as an optimization problem for obtaining point estimates, and provide recommendations on algorithm selection and associated challenges. We then present a systematic framework for employing BO within a Bayesian inference setting, where maximum likelihood–based formulations are extended to characterize parameter uncertainty. The proposed approaches are demonstrated using case studies in both batch and continuous crystallization, covering a range of complexities. Results illustrate the potential of BO to substantially enhance parameter estimation strategies in crystallization modeling, paving the way for its routine integration into parameter estimation and model development workflows.