Higher-order interaction learning of line failure cascading in power networks.

Line failure cascading in power networks is a complex process that involves direct and indirect interactions between lines' states. We consider the inverse problem of learning statistical models to find the sparse interaction graph from the pairwise statistics collected from line failures data in the steady states and over time. We show that the weighted -regularized pairwise maximum entropy models successfully capture pairwise and indirect higher-order interactions undistinguished by observing the pairwise statistics. The learned models reveal asymmetric, strongly positive, and negative interactions between the network's different lines' states. We evaluate the predictive performance of models over independent trajectories of failure unfolding in the network. The static model captures the failures' interactions by maximizing the log-likelihood of observing each link state conditioned to other links' states near the steady states. We use the learned interactions to reconstruct the network's steady states using the Glauber dynamics, predicting the cascade size distribution, inferring the co-susceptible line groups, and comparing the results against the data. The dynamic interaction model is learned by maximizing the log-likelihood of the network's state in state trajectories and can successfully predict the network state for failure propagation trajectories after an initial failure.