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Deep learning has taken part in the competition since not long ago to learnand identify phase transitions in physical systems such as many body quantumsystems, whose underlying lattice structures are generally regular as they'rein euclidean space. Real networks have complex structural features which play asignificant role in dynamics in them, and thus the structural and dynamicalinformation of complex networks can not be directly learned by existing neuralnetwork models. Here we propose a novel and effective framework to learn theepidemic threshold in complex networks by combining the structural anddynamical information into the learning procedure. Considering the strongperformance of learning in Euclidean space, Convolutional Neural Network (CNN)is used and, with the help of confusion scheme, we can identify precisely theoutbreak threshold of epidemic dynamics. To represent the high dimensionalnetwork data set in Euclidean space for CNN, we reduce the dimensionality of anetwork by using graph representation learning algorithms and discretize theembedded space to convert it into an image-like structure. We then creativelymerge the nodal dynamical states with the structural embedding by multi-channelimages. In this manner, the proposed model can draw the conclusion from bothstructural and dynamical information. A large number of simulations show agreat performance in both synthetic and empirical network data set. Ourend-to-end machine learning framework is robust and universally applicable tocomplex networks with arbitrary size and topology.

Learning epidemic threshold in complex networks by Convolutional Neural Network