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Inferring networks from time series: A neural approach.

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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 the dynamics to which they give rise. 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 degree to which the inference problem is underdetermined as well as the noise on the data. This is a feature that other approaches have hitherto been lacking. We demonstrate our method's capabilities by inferring line failure locations in the British power grid from its response to a power cut, providing probability densities on each edge and allowing the use of hypothesis testing to make meaningful probabilistic statements about the location of the cut. Our method is significantly more accurate than both Markov-chain Monte Carlo sampling and least squares regression on noisy data and when the problem is underdetermined, while naturally extending to the case of nonlinear dynamics, which we demonstrate by learning an entire cost matrix for a nonlinear model of economic activity in Greater London. Not having been specifically engineered for network inference, this method in fact represents a general parameter estimation scheme that is applicable to any high-dimensional parameter space.


Acknowledgements: The authors are grateful to Dr Andrew Duncan (Imperial College London) for fruitful discussions on power grid dynamics, and to the anonymous reviewers for their helpful comments during the peer review process.

Funder: Royal Academy of Engineering; DOI:


model calibration, network inference, neural differential equations, power grids

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PNAS Nexus

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Oxford University Press (OUP)
EPSRC (EP/P020720/2)
EPSRC (EP/R018413/2)
EPSRC (via Imperial College London) (EP/T000414/1)
Engineering and Physical Sciences Research Council (EP/R034710/1)