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Numerous studies have demonstrated the ability of Convolutional Neural Networks (CNNs) to classify large numbers of galaxies in a manner that mimics the expertise of astronomers. Such classifications are not always physically motivated, however, such as categorizing galaxies by their morphological types. In this work, we consider the use of CNNs to classify simulated S0 galaxies based on fundamental physical properties. In particular, we undertake two investigations: (1) the classification of simulated S0 galaxies into three distinct evolutionary paths (isolated, tidal interaction in a group halo, and spiral-spiralmerger) and (2) the prediction of the mass ratio for the S0s formed via mergers. To train the CNNs, we first run several hundred N-body simulations to model the formation of S0s under idealized conditions, and then we build our training data sets by creating images of stellar density and two-dimensional kinematic maps for each simulated S0. Our trained networks have remarkable accuracies exceeding 99 per cent when classifying the S0 formation pathway. For the case of predicting merger mass ratios, the mean predictions are consistent with the true values to within roughly one standard deviation across the full range of our data. Our work demonstrates the potential of CNNs to classify galaxies by the fundamental physical properties that drive their evolution.