Perturbative guiding center theory adequately describes the slow drift motion of charged particles in the strongly magnetized regime characteristic of thermal particle populations in various magnetic fusion devices. However, it breaks down for particles with large-enough energy. We report on a data-driven method for learning a nonperturbative guiding center model from full-orbit particle simulation data. We show the data-driven model significantly outperforms traditional asymptotic theory in magnetization regimes appropriate for fusion-born α particles in stellarators, thus opening the door to nonperturbative guiding center calculations.