Data-driven identification of crystallization kinetics

A novel data-driven methodology is presented for developing mathematical models for crystallization processes. The data-driven approach is based on the sparse identification of nonlinear dynamics (SINDy) method, which iterates between a partial least-squares fit and a sparsity-promoting step leading to the discovery of sparse interpretable models. The performance of the SINDy methodology is characterized for the identification of crystallization kinetics in a mixed tank operated in a continuous mode, the isothermal crystallization of lysozyme in a batch stirred tank and cooling crystallization of paracetamol. The SINDy method is robust against noise. Good agreement is obtained between the data-driven model and the data obtained from crystallization experiments. The presented data-driven approach can be attractive for modeling industrial crystallization processes where process analytical technology tools are available for the measurement of process variables but functional forms of kinetic expressions are unknown.