The paper illustrates an adaptive approach based on different topologies of artificial neural networks (ANNs) for the power energy output forecasting of photovoltaic (PV) modules. The analysis of the PV module’s power output needed detailed local climate data, which was collected by a dedicated weather monitoring system. The Department of Energy, Information Engineering, and Mathematical Models of the University of Palermo (Italy) has built up a weather monitoring system that worked together with a data acquisition system. The power output forecast is obtained using three different types of ANNs: a one hidden layer Multilayer perceptron (MLP), a recursive neural network (RNN), and a gamma memory (GM) trained with the back propagation. In order to investigate the influence of climate variability on the electricity production, the ANNs were trained using weather data (air temperature, solar irradiance, and wind speed) along with historical power output data available for the two test modules. The model validation was performed by comparing model predictions with power output data that were not used for the network's training. The results obtained bear out the suitability of the adopted methodology for the short-term power output forecasting problem and identified the best topology.