Research On Phase Transition Of Irreversible Spreading Dynamics On Complex Networks Based On Deep Learning

In recent years,machine learning methods has been widely applied in the field of statistical physics,and gradually applied to solve problems in complex networks.The threshold of SIS and SIR spreading dynamics is similar to the concept of the critical point of phase transition in statistical physics.At present,deep learning methods have studied the threshold recognition of SIS reversible spreading dynamics.In view of this,the thesis mainly focuses on the SIR irreversible spreading dynamics.Multilayer feedforward neural network and convolutional neural network are used to distinguish and analyze the critical point of phase transition(i.e.outbreak threshold).Firstly,this thesis proposes an irreversible spreading threshold's recognition model based on the feature extraction and multi-layer feedforward neural network.The supervised learning and confusion scheme are used in different networks to recognize the threshold from dynamic configuration information of SIR model.However,supervised learning is easily affected by asymmetric data sets,labels' accuracy and random noise.Furthermore,the confusion scheme without prior knowledge is used.However,the feedforward neural network cannot identify the threshold,or even show the phase transition on the synthetic networks and real networks.In view of the heterogeneity or variability of SIR irreversible spreading process near the critical point,the thesis proposes a feature extraction method based on the critical variability.After effective feature extraction,the model can learn the difference of dynamic characteristics of the training set data in different phases.The results on different synthetic networks and real networks show that the method makes the critical recognition model based on confusion scheme perform well.Then,this thesis proposes an irreversible spreading threshold's recognition model based on the feature extraction and poincare embedding.The topological and the dynamic information are combined and converted into a multi-channel image.The model can recognize the threshold of SIS model.However,the convolutional neural network is still unable to learn the difference of the dynamic characteristics near the critical point.Therefore,the dynamic configuration information extracted based on critical features is added to the multi-channel image.The convolutional neural network model recognizes the outbreak threshold precisely in different networks.In addition,the model has a high robustness against random noise and asymmetric data sets,and it can be used without prior knowledge and manual intervention.These above results demonstrate the effectiveness and applicability of the feature extraction method,which provides a new idea and method for the research of phase transition recognition in irreversible spreading dynamics.As the COVID-19 epidemic can be described by the SIR model,the neural network learning model based on feature extraction may have certain reference value for analyzing the development trend of the COVID-19.