Reconstruction of coupling architecture of neural field networks from vector time series

•A new approach to reconstruct couplings in ensembles of oscillators from time series.•Delayed couplings and coupling delay times can be reconstructed.•The approach efficiency is demonstrated numerically for different ensemble size. We propose a method of reconstruction of the network coupling matrix for a basic voltage-model of the neural field dynamics. Assuming that the multivariate time series of observations from all nodes are available, we describe a technique to find coupling constants which is unbiased in the limit of long observations. Furthermore, the method is generalized for reconstruction of networks with time-delayed coupling, including the reconstruction of unknown time delays. The approach is compared with other recently proposed techniques.