Ultracool dwarfs (UCDs, mass M < 0.1 Msun, effective temperature Teff < 3000 K) are the lowest-mass stars and brown dwarfs. They trace the structure, star-formation history and chemical evolution of the Milky Way, due in part to the cooling evolution of non-fusing brown dwarfs. The wide-field optical and infrared spectroscopic and photometric surveys that have uncovered the majority of UCDs now known are generally limited to the local volume (distances < 100 pc) since UCDs are intrinsically faint, however, distant samples are needed to constrain their UCD formation history. Color-selected distant samples of UCDs tend to be contaminated by extra-galactic QSOs at high redshift. To select a sample of spectroscopically-confirmed distant UCDs, we have searched for distant UCDs in 0.5 square degrees of low-resolution near-infrared spectral survey data in the WFC3 Infrared Spectroscopic Parallel Survey (WISPS) and the 3D-HST parallel survey using spectral indices and three supervised machine learning methods: random forest, deep neural network (DNN) and convolutional neural network (CNN). As a training set, we employ a set of known UCD templates from the SpeX Prism Library containing >2,000 low-resolution spectra of UCDs. We achieve a completeness of >94% for the traditional selection methods, and classification precisions of 98%, 96%, 95% for the random forest, DNN and CNN respectively allowing the identification of 231 UCDs out of >250,000 spectra in WISP & 3D-HST. We find that the random forest methods selected the largest number of UCDs with the least amount of contamination. In the future, we will explore different architectures and features for the neural networks to increase their precision.