Adaptive optimisation of noisy black-box functions inherent in microscopic models

For systems where exact constitutive relations are unknown, a microscopic level description can be alternatively used. As microscopic simulations are computationally expensive, there is a need for the development of robust algorithms in order to efficiently optimise such systems taking into consideration the inherent noise associated with the microscopic description. Three optimisation strategies are proposed and tested using a stochastic reaction system as a case study. The first method generates optimal difference intervals to formulate and solve a non-linear program (NLP), whereas the other methods build response surface models and optimise using either a direct search algorithm changing to a steepest descent method once the optimum region is located, or sequential quadratic programming (SQP). The performance of these methods is compared to that of a steepest descent optimisation method commonly used for response surfaces. Their effectiveness is evaluated in terms of the number of microscale function calls and computational time.