The application of the three-component stacked artificial neural network (ANN) for discrimination of dielectric cylinders of different diameters using phase information of synthesized time-domain response is considered. The network consists of two sparse autoencoders and the softmax unit. Neural networks are not tied to the frequency range, unlike many well-known methods based on the resonant properties of objects, and they are a powerful tool for object recognition. In contrast to well-known results, information about the phase of the time-domain signal, which is synthesized from multi-frequency data, is used for discrimination. For ANN training, phase images for cylinders with the radius of 15 to 35 mm are obtained using the method of auxiliary sources (MAS) The possibility of successful recognition was confirmed for the case of the diameter deviation of 1 mm and the presence of additive Gaussian noise with SNR of up to 0 dB.