System identification is the science of modeling dynamical systems from experimental data. The aim of this thesis is to investigate the use of convolutional neural networks (CNNs) in the framework of system identification. More specifically we propose a method to minimize the error defined as the difference between the simulated CNN output and the output sequence experimentally collected on the real system. We formulate the problem in terms of constrained optimization and we solve it by proposing a modified version of the controlled multipliers optimization approach, recently developed by the "System Identification & Control" group at DAUIN. Then, we customize the method to handle two classes of identification problems that motivate the use of CNNs: (i) identification of systems described by partial differential equations and (ii) identification from data collected by taking a video of the physical system under study..