Comparison of multi-fidelity surrogate models for multi-objective aerodynamic optimization in turbomachinery under extreme cost imbalance

Abstract Aerodynamic shape optimization of next-generation aeronautic components faces challenges related to robustness and scalability. Although switching to reliable, albeit expensive, high-fidelity flow models is essential for expanding the design space, the number of high-fidelity simulations that can be performed within the optimization loop is severely limited by computational budget constraints. Furthermore, optimization must handle multiple competing objectives and handle complex constraints in contexts where gradient information is difficult or impossible to retrieve. To address these challenges, we investigate gradient-free, multi-objective constrained optimization strategies based on multi-fidelity surrogate models. In particular, we focus on cases of extreme computational cost imbalance between high- and low-fidelity models, where optimization is driven by a very small number ( O (10)) of high-fidelity simulations. In order to maximize the information extracted from the high-fidelity samples, we first generate a reduced representation of the design space. Next, we consider adaptive infill strategies for actively learning the surrogate using high-fidelity samples that best guide the optimization. Two strategies are proposed and compared: multi-objective constrained Bayesian optimization assisted by a co-kriging surrogate, and a genetic algorithm guided by a multi-fidelity neural network and active learning. The two approaches are evaluated using analytical benchmarks and a realistic use case involving a low-Reynolds linear outlet guide vane cascade, of interest for aeronautical engines. Coarse-mesh RANS simulations are used as the low-fidelity model while RANS simulations with a transition model and automatic mesh adaptation are selected as the high-fidelity ones. The efficacy of the two strategies is measured using various metrics. For the problem under consideration, it has been found that for a small number of high-fidelity samples and after dimension reduction, the Bayesian optimization strategy is more efficient. In the non-reduced design space however, both strategies yield similar performances.