Local approximation to complex models for efficient optimisation: application to crystallisation processes

Recent advances in mathematical modelling have enabled the development of detailed mechanistic models to support the design and analysis of chemical processes or products. However in those cases where the resulting model is highly complex, it can be extremely time consuming to solve the model numerically, thereby limiting its practical applicability. This is especially the case where a complex model is used for the numerical optimisation of a process thereby necessitating the execution of a large number of evaluations of the model. To make such an optimisation task computationally tractable, the idea of approximating complex mechanistic models with statistical models is investigated. In particular, an iterative optimisation procedure is implemented which makes use of a Gaussian process model (GPM) to locally approximate the complex mechanistic model. The GPM is successively updated according to the results obtained from evaluating the original model at locations, in different sub-regions, searched by the optimisation algorithm. The potential of this method in terms of reducing the number of evaluations of the original model, and hence lowering the computational cost, is confirmed through its application to the optimisation of a batch cooling crystallisation process.