There are numerous methods for modeling velocity fields of the Earth’s crust. However, only a few of them are capable of modeling data beyond the contour of the geodetic network (extrapolating). Spatial modeling based on a neural network approach allows for the adequate modeling of the field of recent crustal movements and deformations of the Earth’s crust beyond the geodetic network contour. The study extensively examines the hyperparameter settings and justifies the applicability of the neural network model for predicting crustal movement fields using the Ossetian geodynamic polygon as an example. The presented results, when compared to classical modeling methods, demonstrate that the neural network approach confidently yields results no worse than classical methods. The results of modeling for the Ossetian polygon can be used for geodynamic zoning, identification zones of extension and compression, computing the tectonic component of stresses, and identifying areas of high-gradient displacements.