Groundwater is a vital resource in arid areas that sustains local industrial development and environmental preservation. Mapping groundwater potential zones and determining high-potential regions are essential for the responsible use of the local groundwater resource. When utilizing machine learning or deep learning algorithms to forecast groundwater potential in arid areas, difficulties such as inaccurate and overfitting predictions might occur due to a shortage of borehole samples. In this study, a database of groundwater conditioning factors with a size of 275,157 × 9 was created in the Qaidam Basin, and 85 known borehole samples were collected. The groundwater potential was evaluated using a combination of rank sum ratio (RSR), projection pursuit regression (PPR) and random forest (RF) algorithms, resulting in four models: PPR, RSR-PPR, RSR-RF, and RF. Results indicated that the groundwater potential was higher in mountainous regions surrounding the Qaidam Basin and decreased progressively towards the central and northwestern regions where most industries and facilities are located. The two primary factors, according to the PPR and RF models, were evapotranspiration (0.246, 0.225) and landform (0.176, 0.294). In terms of their ability to accurately forecast the borehole samples, the four models ranked as follows: RF > RSR-RF > RSR-PPR > PPR. The accuracy of the four models in the low-potential area was 0.73 (PPR), 0.60 (RSR-PPR), 0.87 (RSR-RF), and 0.80 (RF), respectively. However, the RF model showed overfitting due to a lack of samples, especially in high-potential regions, which limits its applicability. The RSR-RF method was applied directly to evaluate the entire factor database, avoiding the risk of overfitting caused by a limited number of training samples. The results demonstrate that the RSR-RF model is effective for classifying groundwater potential types in samples and mapping groundwater potential of the study area. This research presents a novel approach for groundwater potential predictions in areas with insufficient sample sizes, providing a reference for policymakers and researchers.