Basin stability (BS) has recently garnered tremendous traction to quantify the reliability of a variety of dynamical systems. In power grid networks, it quantifies the capability of the grid to regain the synchronous state after being perturbated. It is noted that detection of the most vulnerable node or generator with the lowest BS or N-1 reliability is critical toward the optimal decision making on maintenance. However, the conventional estimation of BS relies on the Monte Carlo (MC) method to separate the stable and unstable dynamics originated from the perturbation, which incurs immense computational cost particularly for large-scale networks. As the BS estimate is in essence a classification problem, we investigate the relevance vector machine and active learning to locate the boundary of stable dynamics or the basin of attraction in an efficient manner. This novel approach eschews the large number of sampling points in the MC method and reduces over 95% of the simulation cost in the assessment of N-1 reliability of power grid networks.