Radial velocity estimates provided by Doppler weather radar are critical measurements used by operational forecasters for the detection and monitoring of life-impacting storms. The sampling methods used to produce these measurements are inherently susceptible to aliasing, which produces ambiguous velocity values in regions with high winds and needs to be corrected using a velocity dealiasing algorithm (VDA). In the United States, the Weather Surveillance Radar-1988 Doppler (WSR-88D) Open Radar Product Generator (ORPG) is a processing environment that provides a world-class VDA; however, this algorithm is complex and can be difficult to port to other radar systems outside the WSR-88D network. In this work, a deep neural network (DNN) is used to emulate the two-dimensional WSR-88D ORPG dealiasing algorithm. It is shown that a DNN, specifically a customized U-Net, is highly effective for building VDAs that are accurate, fast, and portable to multiple radar types. To train the DNN model, a large dataset is generated containing aligned samples of folded and dealiased velocity pairs. This dataset contains samples collected from WSR-88D Level-II and Level-III archives and uses the ORPG dealiasing algorithm output as a source of truth. Using this dataset, a U-Net is trained to produce the number of folds at each point of a velocity image. Several performance metrics are presented using WSR-88D data. The algorithm is also applied to other non-WSR-88D radar systems to demonstrate portability to other hardware/software interfaces. A discussion of the broad applicability of this method is presented, including how other Level-III algorithms may benefit from this approach.