The present disclosure provides a system and a method for detecting a fault of an operation of a synchronous motor. The method includes collecting an electrical input and measurements associated with the operation of the synchronous motor caused by the electrical input. The method further includes determining sequences of points defining a mutual position between a stator and a rotor of the synchronous motor that results in magnetostatic determined as a weighted summation over real-space basis functions parameterized on pairs of adjoint points in the determined sequence of points and weighted with a surface charge density between corresponding adjoint points, such that the resulted magnetostatic explains the measurements of the operation of the synchronous motor given the electrical input. Further, the method includes determining the fault of the operation of the synchronous motor based on the mutual position between the stator and the rotor of the synchronous motor.