Groundwater serves as a crucial freshwater resource, especially in arid and semi-arid regions, making accurate predictions essential for sustainable management. This research evaluates and contrasts the effectiveness of four machine learning (ML) techniques in forecasting two key indicators of groundwater sustainability: the groundwater level index (GWLI) and the drought index (DI). The investigated models include Artificial Neural Network (ANN), Adaptive Network-based Fuzzy Inference System (ANFIS), Group Method of Data Handling (GMDH), and Least Squares Support Vector Machine (LSSVM). These models were implemented for the Houmand Absard aquifer in Iran. Historical time-series data were split into training (70%) and testing (30%) sets, with input variables consisting of past groundwater levels (m), precipitation (mm), temperature (degrees C), and evaporation (m) across six unique configurations. Among the evaluated models, GMDH demonstrated the highest predictive accuracy, exhibiting superior correlation coefficients (R), reduced root mean square error (RMSE) and mean absolute error (MAE), and higher Nash-Sutcliffe efficiency (NSE) in both training and testing phases. The GMDH model achieved an average R value of 0.9763 for GWLI and 0.9719 for DI, highlighting its strong predictive capability. These findings underscore the effectiveness of GMDH for short-term groundwater sustainability forecasting and its potential to improve water resource management strategies in the region. Furthermore, results suggest that GMDH slightly outperforms DI in predicting GWLI across all six examined scenarios.