We address the problem of maintaining high voltage power transmission networks in security at all time. This requires that power flowing through all lines remain below a certain nominal thermal limit above which lines might melt, break or cause other damages. Current practices include enforcing the deterministic ``N-1'' reliability criterion, namely anticipating exceeding of thermal limit for any eventual single line disconnection (whatever its cause may be) by running a slow, but accurate, physical grid simulator. New conceptual frameworks are calling for a probabilistic risk based security criterion and are in need of new methods to assess the risk. To tackle this difficult assessment, we address in this paper the problem of rapidly ranking higher order contingencies including all pairs of line disconnections, to better prioritize simulations. We present a novel method based on neural networks, which ranks ``N-1'' and ``N-2'' contingencies in decreasing order of presumed severity. We demonstrate on a classical benchmark problem that the residual risk of contingencies decreases dramatically compared to considering solely all ``N-1'' cases, at no additional computational cost. We evaluate that our method scales up to power grids of the size of the French high voltage power grid (over 1000 power lines).