  There has been recent progress on the problem of inferring the structure of
interactions in complex networks when they are in stationary states satisfying
detailed balance, but little has been done for non-equilibrium systems. Here we
introduce an approach to this problem, considering, as an example, the question
of recovering the interactions in an asymmetrically-coupled,
synchronously-updated Sherrington-Kirkpatrick model. We derive an exact
iterative inversion algorithm and develop efficient approximations based on
dynamical mean-field and Thouless-Anderson-Palmer equations that express the
interactions in terms of equal-time and one time step-delayed correlation
functions.
