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Abstract:
Estimating the outcome of a given dynamical process from structural features is a key unsolved challenge in network science. This goal is hampered by difficulties associated with nonlinearities, correlations and feedbacks between the structure and dynamics of complex systems. In this work, we develop an approach based on machine learning algorithms that provides an important step towards understanding the relationship between the structure and dynamics of networks. In particular, it allows us to estimate from the network structure the outbreak size of a disease starting from a single node, as well as the degree of synchronicity of a system made up of Kuramoto oscillators. We show which topological features of the network are key for this estimation and provide a ranking of the importance of network metrics with much higher accuracy than previously done. For epidemic propagation, the k-core plays a fundamental role, while for synchronization, the betweenness centrality and accessibility are the measures most related to the state of an oscillator. For all the networks, we find that random forests can predict the outbreak size or synchronization state with high accuracy, indicating that the network structure plays a fundamental role in the spreading process. Our approach is general and can be applied to almost any dynamic process running on complex networks. Also, our work is an important step towards applying machine learning methods to unravel dynamical patterns that emerge in complex networked systems.
