Multi-fidelity Bayesian optimization for spatially distributed control of flow over a circular cylinder

Bayesian optimization based on Gaussian process regression has recently spread into a range of computational fluid dynamics problems. It still remains to be explored and developed for the complex flow problems with high dimensions and large computational cost. In this work, we present the application of multi-fidelity Bayesian optimization (MFBO) to drag reduction control of flow over a two-dimensional circular cylinder. The flow is modified by the spatially distributed tangential velocity on the cylinder surface, which is optimized by utilization of MFBO. It is shown that 50% reduction of the computational cost is obtained by using MFBO, as compared with that of single-fidelity Bayesian optimization, by involving low-fidelity simulations. The optimal tangential velocity distribution designed by MFBO is successfully applied to modify the wake of cylinder. As a result, an average drag coefficient reduction rate of 36.2% and decrease in the fluctuation amplitude of lift coefficient by 85.7% at Re = 200 are obtained. Effects of the hyper-parameters of the proposed MFBO control architecture are also examined.