Before revision:  By comparing analytical approximations and exact numerical simulations, we show that the proposed methods provide more accurate estimates for the evolution of equal-time and delayed covariance structures than classical equations, and consequently outperform previous mean field theories for solving the inverse Ising problem.
After revision:  By comparing analytical approximations and exact numerical simulations, we show that the proposed methods provide more accurate estimates of covariance evolution in the system than classical equations, and consequently outperform previous mean field theories for solving the inverse Ising problem.