We develop a method to characterize arbitrary superpositions of light orbital angular momentum (OAM) with high fidelity by using astigmatic transformation and machine-learning processing. In order to identify each superposition unequivocally, we combine two intensity measurements. The first one is the direct image of the input beam, which is invariant for positive and negative OAM components. The second one is an image obtained using an astigmatic transformation, which allows distinguishing between positive and negative topological charges. Samples of these image pairs are used to train a convolution neural network and achieve high-fidelity recognition of arbitrary OAM superpositions.