The design of novel materials hinges on the understanding of structure-property relationships. However, in recent times, our capability to synthesize a large number of materials has outpaced our speed at characterizing them. While the overall chemical constituents can be readily known during synthesis, the structural evolution and characterization of newly synthesized samples remains a bottleneck for the ultimate goal of high throughput nanomaterials discovery. Thus, scalable methods for crystal symmetry determination that can analyze a large volume of material samples within a short time-frame are especially needed. Kikuchi diffraction in the SEM is a promising technique for this due to its sensitivity to dynamical scattering, which may provide information beyond just the seven crystal systems and fourteen Bravais lattices. After diffraction patterns are collected from material samples, deep learning methods may be able to classify the space group symmetries using the patterns as input, which paired with the elemental composition, would help enable the determination of the crystal structure. To investigate the feasibility of this solution, neural networks were trained to predict the space group type of background corrected EBSD patterns. Our networks were first trained and tested on an artificial dataset of EBSD patterns of 5,148 different cubic phases, created through physics-based dynamical simulations. Next, Maximum Classifier Discrepancy, an unsupervised deep learning-based domain adaptation method, was utilized to train neural networks to make predictions for experimental EBSD patterns. We introduce a relabeling scheme, which enables our models to achieve accuracy scores higher than 90% on simulated and experimental data, suggesting that neural networks are capable of making predictions of crystal symmetry from an EBSD pattern.