Phase change materials are of great interest as active layers in rewritable optical disks and novel electronic nonvolatile memories. These applications rest on a fast and reversible transformation between the amorphous and crystalline phases upon heating, taking place on the nanosecond time scale. In this work, we investigate the microscopic origin of the fast crystallization process by means of large-scale molecular dynamics simulations of the phase change compound GeTe. To this end, we use an interatomic potential generated from a Neural Network fitting of a large database of ab initio energies. We demonstrate that in the temperature range of the programming protocols of the electronic memories (500-700 K), nucleation of the crystal in the supercooled liquid is not rate-limiting. In this temperature range, the growth of supercritical nuclei is very fast because of a large atomic mobility, which is, in turn, the consequence of the high fragility of the supercooled liquid and the associated breakdown of the Stokes-Einstein relation between viscosity and diffusivity.