In this paper, we demonstrate two novel data augmentation methods designed to enable the training of a ML–based compact model for an emerging device with extremely limited experimental data. These methods address sparse data and class imbalance, some of the most difficult challenges faced when trying to create a ML-based compact model. In this work, we apply these methods in the creation of an ML-based compact model for the quantum-enhanced Josephson Junction Field Effect Transistor, an emerging quantum-enhanced device with substantial potential but scarce experimental characterization. To account for this, we developed Dynamic Gaussian Noise Data Augmentation (DGNDA), a method of generating additional data points using those already available, and Experimental and Simulation Data Mixing (ESDM), a method of using simulation data to augment the experimental data used for training. DGNDA demonstrated strengthened accuracy in modeling underrepresented classes and ESDM maintained the accuracy of the model comparable to training exclusively on experimental data.