This paper reports a novel non-destructive and non-invasive method to investigate crack formation and propagation in high-performance Nb$_{3}$Sn wires by combining x-ray tomography and deep learning networks. The next generation of high field magnet applications relies on the development of new Nb$_{3}$Sn wires capable to withstand the large stresses generated by Lorentz forces during magnets operation. These stresses can cause a permanent reduction of the transport properties generated by residual deformation of the Nb$_{3}$Sn crystal lattice as well as the formation of cracks in the brittle Nb$_{3}$Sn filaments. Studies for the development of the high luminosity LHC (HL-LHC) upgrade showed that nominal transverse compressive stresses above 150 MPa may be sufficient to generate cracks in the wires. In the case of fusion magnets, wires experience periodic bending due to the electro-magnetic cycles of the reactor which over time may induce wire deformation and filament cracks. Therefore, it has become essential to develop a quantitative method for the characterization of crack formation and propagation under compressive loads. The x-ray tomographic data of a series of restacked-rod-process (RRP) Nb$_{3}$Sn wires was acquired at the micro-tomography beamline ID19 of the European Synchrotron Radiation Facility (ESRF), after intentionally inducing a broad spectrum of cracks in the Nb$_{3}$Sn sub-elements. The samples were submitted to transvers compressive stresses, with and without epoxy impregnation, at different pressures, up to 238 MPa. The resulting tomographic images were analysed by means of deep learning semantic segmentation networks, using U-net, a convolutional neural network (CNN), to identify and segment cracks inside the wires. The trained CNN was able to analyse large volumes of tomographic data, thus enabling a systematic approach for investigating the mechanical damages in Nb$_{3}$Sn wires. We will show the complete three-dimensional reconstruction of various cracks and discuss their impact on the electro-mechanical performance of the analysed wires.