Applying Bayesian Optimization with Gaussian Process Regression to Computational Fluid Dynamics Problems

TL;DR

This paper demonstrates that Bayesian optimization with Gaussian process regression effectively solves diverse CFD problems with high efficiency, requiring relatively few simulations and showing flexibility across different applications.

Contribution

It introduces a versatile BO-GPR approach for CFD optimization that is independent of adjoint methods and compatible with various CFD solvers, reducing computational costs.

Findings

Global optima found with fewer than 90 CFD simulations for up to 8 parameters.

Number of simulations does not significantly increase with more design parameters.

The approach is flexible, efficient, and applicable to practical CFD problems.

Abstract

Bayesian optimization (BO) based on Gaussian process regression (GPR) is applied to different CFD (computational fluid dynamics) problems which can be of practical relevance. The problems are i) shape optimization in a lid-driven cavity to minimize or maximize the energy dissipation, ii) shape optimization of the wall of a channel flow in order to obtain a desired pressure-gradient distribution along the edge of the turbulent boundary layer formed on the other wall, and finally, iii) optimization of the controlling parameters of a spoiler-ice model to attain the aerodynamic characteristics of the airfoil with an actual surface ice. The diversity of the optimization problems, independence of the optimization approach from any adjoint information, the ease of employing different CFD solvers in the optimization loop, and more importantly, the relatively small number of the required flow simulations reveal the flexibility, efficiency, and versatility of the BO-GPR approach in CFD applications. It is shown that to ensure finding the global optimum of the design parameters of the size up to 8, less than 90 executions of the CFD solvers are needed. Furthermore, it is observed that the number of flow simulations does not significantly increase with the number of design parameters. The associated computational cost of these simulations can be affordable for many optimization cases with practical relevance.