  We propose a multi-fidelity neural network (MFNN) tailored for rapid
high-dimensional grid power flow simulations and contingency analysis with
scarce high-fidelity contingency data. The proposed model comprises two
networks -- the first one trained on DC approximation as low-fidelity data and
coupled to a high-fidelity neural net trained on both low- and high-fidelity
power flow data. Each network features a latent module which parametrizes the
model by a discrete grid topology vector for generalization (e.g., $n$ power
lines with $k$ disconnections or contingencies, if any), and the targeted
high-fidelity output is a weighted sum of linear and nonlinear functions. We
tested the model on 14- and 118-bus test cases and evaluated its performance
based on the $n-k$ power flow prediction accuracy with respect to imbalanced
contingency data and high-to-low-fidelity sample ratio. The results presented
herein demonstrate MFNN's potential and its limits with up to two orders of
magnitude faster and more accurate power flow solutions than DC approximation.
