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A novel approach is presented for efficiently training a neural network (NN)-based surrogate model when the training data set is to be generated using a computationally intensive high-fidelity computational model. The approach consists in using a Gaussian Process (GP), and more specifically, its acquisition function, to adaptively sample the parameter space of interest and generate the minimum amount of training data needed to achieve the desired level of approximation accuracy. The overall approach is explained and illustrated with numerical experiments associated with the prediction of the lift-over-drag ratio for a NACA airfoil in a large, two-dimensional parameter space of free-stream Mach number and free-stream angle of attack. The obtained numerical results demonstrate the superior accuracy delivered by the proposed training over standard trainings using uniform and random samplings.

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