  Network controllability robustness reflects how well a networked system can
maintain its controllability against destructive attacks. Its measure is
quantified by a sequence of values that record the remaining controllability of
the network after a sequence of node-removal or edge-removal attacks.
Traditionally, the controllability robustness is determined by attack
simulations, which is computationally time consuming or even infeasible. In the
present paper, an improved method for predicting the network controllability
robustness is developed based on machine learning using a group of
convolutional neural networks (CNNs). In this scheme, a number of training data
generated by simulations are used to train the group of CNNs for classification
and prediction, respectively. Extensive experimental studies are carried out,
which demonstrate that 1) the proposed method predicts more precisely than the
classical single-CNN predictor; 2) the proposed CNN-based predictor provides a
better predictive measure than the traditional spectral measures and network
heterogeneity.
