Deep Learning Super-Diffusion in Multiplex Networks

Abstract

Complex network theory has shown success in understanding the emergent and collective behavior of complex systems [1]. Many real-world complex systems were recently discovered to be more accurately modeled as multiplex networks [2-6]-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 superdiffusion: 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 which has developed techniques to recognize, classify, and characterize complex sets of data. We show that modern machine learning architectures, such as fully connected and convolutional neural networks, 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.

Predicting quantum advantage by quantum walk with convolutional neural networks

“…Here we use a CNN for graph features extraction and learning the most relevant features, which we apply to a classification problem defined within the quantum walk framework. CNNs were recently used with graph adjacently matrix input for predicting clinical neurodevelopmental outcomes from brain networks [65] and for classifying and predicting the presence of super-diffusion in multiplex networks [66].…”