  Higher variability in grid conditions, resulting from growing renewable
penetration and increased incidence of extreme weather events, has increased
the difficulty of screening for scenarios that may lead to catastrophic
cascading failures. Traditional power-flow-based tools for assessing cascading
blackout risk are too slow to properly explore the space of possible failures
and load/generation patterns. We add to the growing literature of faster
graph-neural-network (GNN)-based techniques, developing two novel techniques
for the estimation of blackout magnitude from initial grid conditions. First we
propose several methods for employing an initial classification step to filter
out safe "non blackout" scenarios prior to magnitude estimation. Second, using
insights from the statistical properties of cascading blackouts, we propose a
method for facilitating non-local message passing in our GNN models. We
validate these two approaches on a large simulated dataset, and show the
potential of both to increase blackout size estimation performance.
