In this paper, a neural network approach is applied for solving an electromagnetic inverse problem involving solid dielectric materials subjected to shock impacts and interrogated by a millimeter-wave interferometer. Under mechanical impact, a shock wave is generated in the material and modifies the refractive index. It was recently demonstrated that the shock wavefront velocity and the particle velocity as well as the modified index in a shocked material can be remotely derived from measuring two characteristic Doppler frequencies in the waveform delivered by a millimeter-wave interferometer. We show here that a more accurate estimation of the shock wavefront and particle velocities can be obtained from training an appropriate convolutional neural network, especially in the important case of short-duration waveforms of few microseconds.