  Semidefinite programming is an important optimization task, often used in
time-sensitive applications. Though they are solvable in polynomial time, in
practice they can be too slow to be used in online, i.e. real-time
applications. Here we propose to solve feasibility semidefinite programs using
artificial neural networks. Given the optimization constraints as an input, a
neural network outputs values for the optimization parameters such that the
constraints are satisfied, both for the primal and the dual formulations of the
task. We train the network without having to exactly solve the semidefinite
program even once, thus avoiding the possibly time-consuming task of having to
generate many training samples with conventional solvers. The neural network
method is only inconclusive if both the primal and dual models fail to provide
feasible solutions. Otherwise we always obtain a certificate, which guarantees
false positives to be excluded. We examine the performance of the method on a
hierarchy of quantum information tasks, the Navascu\'es-Pironio-Ac\'in
hierarchy applied to the Bell scenario. We demonstrate that the trained neural
network gives decent accuracy, while showing orders of magnitude increase in
speed compared to a traditional solver.
