Learning epidemic threshold in complex networks by Convolutional Neural Network.

Deep learning has taken part in the competition since not long ago to learn and identify phase transitions in physical systems such as many-body quantum systems, whose underlying lattice structures are generally regular as they are in Euclidean space. Real networks have complex structural features that play a significant role in dynamics in them, and thus the structural and dynamical information of complex networks cannot be directly learned by existing neural network models. Here, we propose a novel and effective framework to learn the epidemic threshold in complex networks by combining the structural and dynamical information into the learning procedure. Considering the strong performance of learning in Euclidean space, the Convolutional Neural Network (CNN) is used, and, with the help of "confusion scheme," we can identify precisely the outbreak threshold of epidemic dynamics. To represent the high-dimensional network data set in Euclidean space for CNN, we reduce the dimensionality of a network by using graph representation learning algorithms and discretize the embedded space to convert it into an imagelike structure. We then creatively merge the nodal dynamical states with the structural embedding by multichannel images. In this manner, the proposed model can draw the conclusion from both structural and dynamical information. A large number of simulations show a great performance in both synthetic and empirical network data sets. Our end to end machine learning framework is robust and universally applicable to complex networks with arbitrary size and topology.