We present the application of convolutional neural networks to a particular problem in gamma ray astronomy. Explicitly, we use this method to investigate the origin of an excess emission of GeV γ rays in the direction of the Galactic Center, reported by several groups by analyzing Fermi-LAT data. Interpretations of this excess include γ rays created by the annihilation of dark matter particles and γ rays originating from a collection of unresolved point sources, such as millisecond pulsars. We train and test convolutional neural networks with simulated Fermi-LAT images based on point and diffuse emission models of the Galactic Center tuned to measured γ ray data. Our new method allows precise measurements of the contribution and properties of an unresolved population of γ ray point sources in the interstellar diffuse emission model. The current model predicts the fraction of unresolved point sources with an error of up to 10% and this is expected to decrease with future work.