Three artificial neural network learning algorithms were utilized to forecast the productivity (MD) of a solar still operating in a hyper-arid environment. The learning algorithms were the Levenberg–Marquardt (LM), the conjugate gradient backpropagation with Fletcher–Reeves restarts, and the resilient backpropagation. The Julian day, ambient air temperature, relative humidity, wind speed, solar radiation, temperature of feed water, temperature of brine water, total dissolved solids (TDS) of feed water, and TDS of brine water were used in the input layer of the developed neural network model. The MD was located in the output layer. The developed model for each algorithm was trained, tested, and validated with experimental data obtained from field experimental work. Findings revealed the developed model could be utilized to predict the MD with excellent accuracy. The LM algorithm (with a minimum root mean squared error and a maximum overall index of model performance) was found to be the best in the training, testing, and validation stages. Relative errors in the predicted MD values of the developed model using the LM algorithm were mostly in the vicinity of ±10%. These results indicated that the LM algorithm is the most ideal and accurate algorithm for the prediction of the MD with the developed model.