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Hydrogen production using polymer membrane electrolyzers is an effective and valuable way of generating an environmentally friendly energy source. Hydrogen and oxygen generated by electrolyzers can power drone fuel cells. The thermodynamic analysis of polymer membrane electrolyzers to identify key losses and optimize their performance is fundamental and necessary. In this article, the process of the electrolysis of water by a polymer membrane electrolyzer in combination with a concentrated solar system in order to generate power and hydrogen was studied, and the effect of radiation intensity, current density, and other functional variables on the hydrogen production was investigated. It was shown that with an increasing current density, the voltage generation of the electrolyzer increased, and the energy efficiency and exergy of the electrolyzer decreased. Additionally, as the temperature rose, the pressure dropped, the thickness of the Nafion membrane increased, the voltage decreased, and the electrolyzer performed better. By increasing the intensity of the incoming radiation from 125 W/m2 to 320 W/m2, the hydrogen production increased by 111%, and the energy efficiency and exergy of the electrolyzer both decreased by 14% due to the higher ratio of input electric current to output hydrogen. Finally, machine-learning-based predictions were conducted to forecast the energy efficiency, exergy efficiency, voltage, and hydrogen production rate in different scenarios. The results proved to be very accurate compared to the analytical results. Hyperparameter tuning was utilized to adjust the model parameters, and the models’ results showed an MAE lower than 1.98% and an R2 higher than 0.98.