This article presents two neural network approaches for estimating the covariance function of a spatial Gaussian random field defined in a portion of the euclidean plane. Our proposal builds upon recent contributions, expanding from the purely isotropic setting to encompass geometrically anisotropic correlation structures, i.e. random fields with correlation ranges that vary across different directions. We conduct experiments with both simulated and real data to assess the performance of the methodology and to provide guidelines to practitioners.