  In this study, we analyzed the problem of accelerating the linear average
consensus algorithm for complex networks. We propose a data-driven approach to
tuning the weights of temporal (i.e., time-varying) networks using deep
learning techniques. Given a finite-time window, the proposed approach first
unfolds the linear average consensus protocol to obtain a feedforward
signal-flow graph, which is regarded as a neural network. The edge weights of
the obtained neural network are then trained using standard deep learning
techniques to minimize consensus error over a given finite-time window. Through
this training process, we obtain a set of optimized time-varying weights, which
yield faster consensus for a complex network. We also demonstrate that the
proposed approach can be extended for infinite-time window problems. Numerical
experiments revealed that our approach can achieve a significantly smaller
consensus error compared to baseline strategies.
