Variations on bayesian optimization applied to numerical flow simulations

Abstract

Bayesian Optimization (BO) has recently regained interest in optimization problems involving expensive black-box objective functions. Several variants have been proposed in the literature, such as including gradient and/or multi-fidelity information, and it has been extended to multi-objective optimization problems. Despite its recent applications to numerical flow simulations, the efficiency of this method and its variants remains to be characterized in typical applications involving canonical flows.

In this work, the efficiency of classical BO and alternative derivative-free methods is compared on a simplified flow case, i.e. drag reduction in the two-dimensional flow around a cylinder. The application of BO to complex flows is then showcased by considering a three-dimensional case at Reynolds number Re = 3900. Next, the performance of BO with gradient and/or multi-fidelity information is investigated for global modelling and optimization on typical benchmark objective functions and on the cylinder case at Re = 200. Finally, an algorithm combining dimension reduction and Multi-objective Bayesian Optimization (MOBO) is proposed.

It is found that BO was more efficient than other derivative-free alternatives and showed promising results on the three-dimensional cylinder at Re = 3900 by reducing drag by 23 %. The performance of the algorithm was further improved when multi-fidelity and/or gradient information was included, both for modelling and optimization. Including gradient information on the low-fidelity model was useful for global modelling and to decrease rapidly the objective function in a BO framework. On the contrary, adding derivative information on the high-fidelity model generally gave the most accurate approximation of the minimum but was inefficient for global modelling when the computational cost of the gradient was high. Finally, the developed algorithm combining dimension reduction and MOBO enabled us to obtain more precise and diverse minima.