Plate and spring reverberators are electromechanical systems first used and researched as means to substitute real room reverberation. Nowadays they are often used in music production for aesthetic reasons due to their particular sonic characteristics. The modeling of these audio processors and their perceptual qualities is difficult since they use mechanical elements together with analog electronics resulting in an extremely complex response. Based on digital reverberators that use sparse FIR filters, we propose a signal processing-informed deep learning architecture for the modeling of artificial reverberators. We explore the capabilities of deep neural networks to learn such highly nonlinear electromechanical responses and we perform modeling of plate and spring reverberators. In order to measure the performance of the model, we conduct a perceptual evaluation experiment and we also analyze how the given task is accomplished and what the model is actually learning.