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A multi-fidelity (MF) active learning method is presented for designoptimization problems characterized by noisy evaluations of the performancemetrics. Namely, a generalized MF surrogate model is used for design-spaceexploration, exploiting an arbitrary number of hierarchical fidelity levels,i.e., performance evaluations coming from different models, solvers, ordiscretizations, characterized by different accuracy. The method is intended toaccurately predict the design performance while reducing the computationaleffort required by simulation-driven design (SDD) to achieve the globaloptimum. The overall MF prediction is evaluated as a low-fidelity trainedsurrogate corrected with the surrogates of the errors between consecutivefidelity levels. Surrogates are based on stochastic radial basis functions(SRBF) with least squares regression and in-the-loop optimization ofhyperparameters to deal with noisy training data. The method adaptively queriesnew training data, selecting both the design points and the required fidelitylevel via an active learning approach. This is based on the lower confidencebounding method, which combines performance prediction and associateduncertainty to select the most promising design regions. The fidelity levelsare selected considering the benefit-cost ratio associated with their use inthe training. The method's performance is assessed and discussed using fouranalytical tests and three SDD problems based on computational fluid dynamicssimulations, namely the shape optimization of a NACA hydrofoil, the DTMB 5415destroyer, and a roll-on/roll-off passenger ferry. Fidelity levels are providedby both adaptive grid refinement and multi-grid resolution approaches. Underthe assumption of a limited budget of function evaluations, the proposed MFmethod shows better performance in comparison with the model trained byhigh-fidelity evaluations only.

A Multi-Fidelity Active Learning Method for Global Design Optimization Problems with Noisy Evaluations