Popov’s simple formula for the coefficient of friction, which was recently introduced as a generalization of Coulomb’s empirical relations between the friction coefficient and one or the other external parameter (including normal load, sliding velocity, and size of contact), is represented in terms of artificial neural networks (ANNs). The ANN-based schematic of Popov’s formula is used as an inspiration for creating a novel ANN model designed for capturing intrinsic dependencies from the four-dimensional data set (experimentally measured coefficient of friction versus discrete values of the three external parameters). A two-step training process is assumed by utilizing the two-dimensional data sets (coefficient of friction versus values of only one external parameter while others are fixed) for pre-training the corresponding subnetworks.