We simulate the coherent stage of Cu precipitation in α-Fe with an atomistic kinetic Monte Carlo (AKMC) model. The vacancy migration energy as a function of the local chemical environment is provided on-the-fly by a neural network, trained with high precision on values calculated with the nudged elastic band method, using a suitable interatomic potential. To speed up the simulation, how- ever, we modify the standard AKMC algorithm by treating large Cu clusters as objects, similarly to object kinetic Monte Carlo approaches. Seamless matching between the fully atomistic and the coarse-grained approach is achieved again by using a neural network, that provides all stability and mobility parameters for large Cu clusters, after training on atomistically informed results. The result- ing hybrid algorithm allows long thermal annealing experiments to be simulated, within a reasonable CPU time. The results obtained are in very good agreement with several series of experimental data available from the literature, spanning over different conditions of temperature and alloy composi- tion. We deduce from these results and relevant parametric studies that the mobility of Cu clusters containing one vacancy plays a central role in the precipitation mechanism.