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 SK model. We derive an exact iterative inversion
algorithm and develop efficient approximations based on dynamical
mean-field and TAP equations that express the interactions in terms
of equal-time and one time step-delayed correlation functions.