Multi-Fidelity Adaptive Sampling for Surrogate-Based Optimization and Uncertainty Quantification

Surrogate-based algorithms are indispensable in the aerospace engineering field for reducing the computational cost of optimization and uncertainty quantification analyses, particularly those involving computationally intensive solvers. This paper presents a novel approach for enhancing the efficiency of surrogate-based algorithms through a new multi-fidelity sampling technique. Unlike existing multi-fidelity methods which are based on a single multiplicative acquisition function, the proposed technique decouples the identification of the new infill sample from the selection of the fidelity level. The location of the infill sample is determined by leveraging the highest fidelity surrogate model, while the fidelity level used for its performance evaluation is chosen as the cheapest one within the "accurate enough" models at the infill location. Moreover, the methodology introduces the application of the Jensen-Shannon divergence to quantify the accuracy of the different fidelity levels. Overall, the resulting technique eliminates some of the drawbacks of existing multiplicative acquisition functions such as the risk of continuous sampling from lower and cheaper fidelity levels. Experimental validation conducted in surrogate-based optimization and uncertainty quantification scenarios demonstrates the efficacy of the proposed approach. In an aerodynamic shape optimization task focused on maximizing the lift-to-drag ratio, the multi-fidelity strategy achieved comparable results to standard single-fidelity sampling but with approximately a five-fold improvement in computational efficiency. Likewise, a similar reduction in computational costs was observed in the uncertainty quantification problem, with the resulting statistical values aligning closely with those obtained using traditional single-fidelity sampling.