We propose a methodology for predicting migration energies associated to the migration of single atoms towards vacant sites, using artificial neural networks. The novelty of the approach, which has already been proven efficient for bulk materials (e.g. bcc or fcc Fe-based alloys), is to allow for any structure, without restriction to a specific lattice. The proposed technique is designed in conjunction with a novel kind of lattice-free atomistic kinetic Monte Carlo model. The idea is to avoid as much as possible heavy atomistic simulations, e.g. static relaxation or general methods for finding transition paths. Such calculations, however, are applied once per Monte Carlo event, when a selected event is applied. The objective of this work is thus to propose a methodology for defining migration events at every step of the simulation, and at the same time assigning a frequency of occurrence to them (using artificial neural networks), in short computing times. We demonstrate the feasibility of this new concept by designing neural networks for predicting vacancy migration energies near grain boundaries in bcc FeCr alloys.