  To shift the computational burden from real-time to offline in delay-critical
power systems applications, recent works entertain the idea of using a deep
neural network (DNN) to predict the solutions of the AC optimal power flow
(AC-OPF) once presented load demands. As network topologies may change,
training this DNN in a sample-efficient manner becomes a necessity. To improve
data efficiency, this work utilizes the fact OPF data are not simple training
labels, but constitute the solutions of a parametric optimization problem. We
thus advocate training a sensitivity-informed DNN (SI-DNN) to match not only
the OPF optimizers, but also their partial derivatives with respect to the OPF
parameters (loads). It is shown that the required Jacobian matrices do exist
under mild conditions, and can be readily computed from the related primal/dual
solutions. The proposed SI-DNN is compatible with a broad range of OPF solvers,
including a non-convex quadratically constrained quadratic program (QCQP), its
semidefinite program (SDP) relaxation, and MATPOWER; while SI-DNN can be
seamlessly integrated in other learning-to-OPF schemes. Numerical tests on
three benchmark power systems corroborate the advanced generalization and
constraint satisfaction capabilities for the OPF solutions predicted by an
SI-DNN over a conventionally trained DNN, especially in low-data setups.
