Selective area electron diffraction (SAED) patterns can provide valuable insight into the structure of a material. However, the manual identification of collected patterns can be a significant bottleneck in the overall phase classification workflow. In this work, we utilize the recent advances in computer vision and machine learning (ML) to automate the indexing of SAED patterns. The performance of six different ML algorithms is demonstrated using metallic plutonium-zirconium alloys. The most successful approach trained a neural network (NN) to make a classification of the phase and zone axis, and then utilized a second NN to synthesize multiple independent predictions of different tilts in a single sample to make an overall phase identification. The results demonstrate that automated SAED phase identification using ML is a viable route to accelerate materials characterization.