Deep Learning Phase Transition Of Epidemic Dynamics On Complex Networks

In recent years,more and more researches are devoted to applying machine learning methods to the identification of phase transition thresholds of Ising models in the field of statistical physics.The dynamics of SIS epidemics on complex networks has some similarities with the dynamics of the Ising model,e.g.,there being two phases in these two dynamics,each node having two states,and there occurring second-order phase transition.But currently there are few related studies.Since the research on the identification of epidemic threshold on complex networks has always been a hot and unavoidable topic,this thesis mainly studies the adaptability of deep learning methods to this problem,and proposes two models based on feed-forward neural network and convolutional neural network,respectivelyFirstly,this thesis proposes a threshold recognition model based on feed-forward neural network.The model can identify the threshold of SIS model through supervised learning or "confusion scheme".The idea based on supervised learning is straightforward and simple,and has achieved good results in some network structures However,the method based on supervised learning is not robust,and is susceptible to the symmetry of the data set and the accuracy of the labels.In order to improve the stability of the model,this article uses a method that combines supervised learning and unsupervised learning:"confusion scheme",which makes the model get rid of the dependence on prior knowledge and improves the learning performance.In some heterogeneous networks,due to the presence of large-degree nodes,the dynamical information is mainly concentrated on these hub nodes,and the information of a large number of small-degree nodes will reduce the influence of the large-scale node information,resulting in a worse learning effect.In this thesis,two network sampling methods based on the node importance are proposed to strengthen the dynamical information on important nodes,and they have achieved good learning effects on networks with various structuresSecondly,in view of the defect that the feed-forward neural network cannot learn the structural information of the network,this thesis proposes another model based on the convolutional neural network.Since the learning effect of the convolutional neural network on the picture-like structure is outstanding,we use the network representation learning method to convert the network into a two-dimensional picture,and then add dynamical information to the picture through a multi-channel method.At this point,the convolutional neural network can easily learn these network dimensionality reduction representations with dynamical information,and the "confusion scheme" method can get more accurate threshold recognition results.Many experiments show that the model based on the convolutional neural network has high robustness,without any prior knowledge and manual intervention,and can simultaneously learn the topological information and dynamical information of complex networksThe threshold recognition model proposed in this thesis is a brand-new attempt in the field of combining complex networks with machine learning,which provides a new idea for the follow-up researches on this hot issue.At the same time,this work is valuable for the identification of phase transition of network dynamics on complex networks.