Global approximation models are often used in design and analysis activities in lieu of expensive simulations. Surrogate modeling with adaptive sampling is an efficient approach for creating these global models. There is a growing interest in global neural network (NN) modeling since it can approximate complex functions and can handle large datasets. Hence, this work proposes a novel method, called separate adaptive sampling (SAS), for creating global models using NNs. SAS performs exploration and exploitation using two criteria, unlike existing methods which use a single criterion. An exploration point is obtained from a space-filling sampling algorithm, while an exploitation point is obtained by maximizing the uncertainty in the NN prediction. Three existing global modeling algorithms are used for comparison. These algorithms are demonstrated on three test cases. The first two test cases are analytical functions with 3 and 8 dimensions, while the third test case is a physics-based airfoil modeling problem consisting of 16 dimensions. SAS performs best for the analytical cases while achieving comparable performance for the third case. Moreover, the NN training time for each method is nearly constant as the number of samples increase.