Bayesian optimization of gray-box process models using a modified upper confidence bound acquisition function

Optimizing complex process models can be challenging due to the computation time required to solve the model equations. A popular technique is to replace difficult-to-evaluate submodels with surrogate models, creating a gray-box process model. Bayesian optimization (BO) is effective for global optimization with minimal function evaluations. However, existing extensions of BO to gray-box models rely on Monte Carlo (MC) sampling, which requires preselecting the number of MC samples, adding complexity. In this paper, we present a novel BO approach for gray-box process models that uses sensitivities instead of MC and can be used to exploit decoupled problems, where multiple submodels can be evaluated independently. The new approach is successfully applied to six benchmark test problems and to a realistic chemical process design problem. It is shown that the proposed methodology is more efficient than other methods and that exploiting the decoupled case additionally reduces the number of required submodel evaluations.