The dislocation activity controls the plastic deformation in the most of metallic materials. Mechanical loading with high strain rates or with high strain gradients can lead to either homogeneous nucleation of the dislocation or emission of dislocations from various heterogeneities, such as nanopores and phase precipitates. The dislocation nucleation and emission trigger plasticity, which relaxes the shear component of stresses. In this work, we study the threshold of dislocation emission from nanosized copper inclusions in an aluminum single crystal in comparison with the homogeneous nucleation of dislocations in pure metal. We consider different shapes of inclusions (spherical, cylindrical and cubic) and rather arbitrary axisymmetric deformations by means of molecular dynamics (MD) simulations. For most deformation paths, the copper inclusions substantially reduce the threshold of plasticity incipience, while the inclusions have no effect for some deformation paths with either axial or transverse extension. Depending on the deformation path, the shape of inclusion can either influence the emission threshold or not. Thus, there is a complex dependence of the threshold of plasticity incipience on the deformation path, the presence and the form of copper inclusions. This dependence is approximated by means of an artificial neural network (ANN) trained on the results of MD simulations. The trained ANN can be further applied as a constitutive equation at the level of continuum mechanics.