  Network robustness is critical for various societal and industrial networks
again malicious attacks. In particular, connectivity robustness and
controllability robustness reflect how well a networked system can maintain its
connectedness and controllability against destructive attacks, which can be
quantified by a sequence of values that record the remaining connectivity and
controllability of the network after a sequence of node- or edge-removal
attacks. Traditionally, robustness is determined by attack simulations, which
are computationally very time-consuming or even practically infeasible. In this
paper, an improved method for network robustness prediction is developed based
on learning feature representation using convolutional neural network
(LFR-CNN). In this scheme, higher-dimensional network data are compressed to
lower-dimensional representations, and then passed to a CNN to perform
robustness prediction. Extensive experimental studies on both synthetic and
real-world networks, both directed and undirected, demonstrate that 1) the
proposed LFR-CNN performs better than other two state-of-the-art prediction
methods, with significantly lower prediction errors; 2) LFR-CNN is insensitive
to the variation of the network size, which significantly extends its
applicability; 3) although LFR-CNN needs more time to perform feature learning,
it can achieve accurate prediction faster than attack simulations; 4) LFR-CNN
not only can accurately predict network robustness, but also provides a good
indicator for connectivity robustness, better than the classical spectral
measures.
