Deep learning super-diffusion in multiplex networks

Abstract

Complex network theory has shown success in understanding the emergent and collective behavior of complex systems Newman 2010 Networks: An Introduction (Oxford: Oxford University Press). Many real-world complex systems were recently discovered to be more accurately modeled as multiplex networks Bianconi 2018 Multilayer Networks: Structure and Function (Oxford: Oxford University Press); Boccaletti et al 2014 Phys. Rep. 544 1–122; Lee et al 2015 Eur. Phys. J. B 88 48; Kivelä et al 2014 J. Complex Netw. 2 203–71; De Domenico et al 2013 Phys. Rev. X 3 041022—in which each interaction type is mapped to its own network layer; e.g. multi-layer transportation networks, coupled social networks, metabolic and regulatory networks, etc. A salient physical phenomena emerging from multiplexity is super-diffusion: exhibited by an accelerated diffusion admitted by the multi-layer structure as compared to any single layer. Theoretically super-diffusion was only known to be predicted using the spectral gap of the full Laplacian of a multiplex network and its interacting layers. Here we turn to machine learning (ML) which has developed techniques to recognize, classify, and characterize complex sets of data. We show that modern ML architectures, such as fully connected and convolutional neural networks (CNN), can classify and predict the presence of super-diffusion in multiplex networks with 94.12% accuracy. Such predictions can be done in situ, without the need to determine spectral properties of a network.

mGNN: Generalizing the Graph Neural Networks to the Multilayer Case

“…In this section we demonstrate how our framework can be used to reproduce the results from V.M. Leli et al [60], who predict whether a multiplex network exhibits superdiffusion or not, and do so with a classical Deep Learning model employing CNNs (convolutional neural networks) on the supra-adjacency matrix. The main limitations of their work are that the models, once trained, are not able to generalize to networks with different number of nodes and layers, and that the models require a lot of training examples.…”