Inference of Kinetics in Population Balance Models using Gaussian Process Regression

Population balance models are used to describe systems composed of individual entities dispersed in a continuous phase. Identification of system dynamics is an essential yet difficult step in the modeling of population systems. In this paper, Gaussian processes are utilized to infer kinetics of a population model, including interaction with a continuous phase, from measurements via non-parametric regression. Under a few conditions, it is shown that the population kinetics in the process model can be estimated from the moment dynamics, rather than the entire population distribution. The method is illustrated with a numerical case study regarding crystallization, in order to infer growth and nucleation rates from varying noise-induced simulation data.