Acoustic tones can impede safe store separation and amplify structural fatigue in airborne military aircraft with open internal bays. Experimentally simulating such cavity flows is essential to understanding the physical phenomena. This study will demonstrate that a machine learning algorithm can accurately classify flow regimes using a limited number of data points and help identify regions of interest for future experiments. McKay's Latin hypercube method was used to select the best data points from a database comprised of the experimental results of tests conducted in the NASA Langley eight-foot transonic pressure tunnel on a variable geometry rectangular cavity. A Galerkin-derived, adaptive, matrix-free scattered data approximation scheme based on artificial neural networks, called Sequential Function Approximation, was trained using the best data subsets and then used to predict the results of the wind tunnel experiments. We first determined whether Sequential Function Approximation could predict the three classes of observed cavity flow. Then, we used our algorithm to predict both flow class and the occurrence of acoustic resonance. These results favorably compared against solutions from publicly-available support vector machines and pre-built classifier programs.