The interpolation of GPS velocity vectors into continuous fields represents a significant challenge in geodesy and geophysics. Conventional methods, such as the elastic Green's function proposed by Sandwell and Wessel (2016), face limitations in modeling complex phenomena and accounting for data uncertainties. This paper investigates the application of Physics-Informed Neural Networks as a powerful alternative to these classical methods. In this study, a PINN model was implemented that directly incorporates the governing equations of elasticity into the Neural Network's loss function. The model was trained on GPS data from 89 stations across the Alborz Tectonic Region in the oblique collision zone of the Arabia-Eurasia tectonic plates. Results demonstrate that the proposed model can successfully reconstruct the velocity field with acceptable accuracy, achieving RMSE values of approximately 0.68 mm/yr and 0.99 mm/yr for the east and north components, respectively. The method offers several advantages, including high flexibility in modeling complex physics, the capability to integrate diverse data types, and automatic consideration of observational uncertainties. Although the computational time of this approach is longer compared to classical methods, its inherent ability to overcome the limitations of traditional techniques makes it a promising candidate for the next generation of geodynamic data processing tools.