In solar parabolic-trough plants, the use of Model Predictive Control (MPC) increases the output thermal power. However, MPC has the disadvantage of a high computational demand that hinders its application to some processes. This work proposes using artificial neural networks to approximate the optimal flow rate given by an MPC controller to decrease the computational load drastically to a 3% of the MPC computation time. The neural networks have been trained using a 30-day synthetic dataset of a collector field controlled by MPC. The use of a different number of measurements as inputs to the network has been analyzed. The results show that the neural network controllers provide practically the same mean power as the MPC controller with differences under 0.02 kW for most neural networks, less abrupt changes at the output and slight violations of the constraints. Moreover, the proposed neural networks perform well, even using a low number of sensors and predictions, decreasing the number of neural network inputs to 10% of the original size.European Research Council. Advanced Grant OCONTSOLAR number789051Ministerio de Ciencia, Innovación y Universidades IJC2018-035395-