  The dynamics of power grids are governed by a large number of nonlinear
differential and algebraic equations (DAEs). To safely operate the system,
operators need to check that the states described by these DAEs stay within
prescribed limits after various potential faults. However, current numerical
solvers of DAEs are often too slow for real-time system operations. In
addition, detailed system parameters are often not exactly known. Machine
learning approaches have been proposed to reduce computational efforts, but
existing methods generally suffer from overfitting and failures to predict
unstable behaviors.
  This paper proposes a novel framework to predict power system transients by
learning in the frequency domain. The intuition is that although the system
behavior is complex in the time domain, there are relatively few dominant modes
in the frequency domain. Therefore, we learn to predict by constructing neural
networks with Fourier transform and filtering layers. System topology and fault
information are encoded by taking a multi-dimensional Fourier transform,
allowing us to leverage the fact that the trajectories are sparse both in time
and spatial frequencies. We show that the proposed approach does not need
detailed system parameters, greatly speeds up prediction computations and is
highly accurate for different fault types.
