Inferring networks from time series: a neural approach

Network structures underlie the dynamics of many complex phenomena, from gene regulation and foodwebs to power grids and social media. Yet, as they often cannot be observed directly, their connectivities must be inferred from observations of their emergent dynamics. In this work we present a powerful computational method to infer large network adjacency matrices from time series data using a neural network, in order to provide uncertainty quantification on the prediction in a manner that reflects both the non-convexity of the inference problem as well as the noise on the data. This is useful since network inference problems are typically underdetermined, and a feature that has hitherto been lacking from such methods. We demonstrate our method's capabilities by inferring line failure locations in the British power grid from its response to a power cut. Since the problem is underdetermined, many classical statistical tools (e.g. regression) will not be straightforwardly applicable. Our method, in contrast, provides probability densities on each edge, allowing the use of hypothesis testing to make meaningful probabilistic statements about the location of the power cut. We also demonstrate our method's ability to learn an entire cost matrix for a non-linear model of economic activity in Greater London. Our method outperforms OLS regression on noisy data in terms of both speed and prediction accuracy, and scales as $N^2$ where OLS is cubic. Not having been specifically engineered for network inference, our method represents a general parameter estimation scheme that is applicable to any parameter dimension.