  The simulation of complex stochastic network dynamics arising, for instance,
from models of coupled biomolecular processes remains computationally
challenging. Often, the necessity to scan a models' dynamics over a large
parameter space renders full-fledged stochastic simulations impractical,
motivating approximation schemes. Here we propose an approximation scheme which
improves upon the standard linear noise approximation while retaining similar
computational complexity. The underlying idea is to minimize, at each time
step, the Kullback-Leibler divergence between the true time evolved probability
distribution and a Gaussian approximation (entropic matching). This condition
leads to ordinary differential equations for the mean and the covariance matrix
of the Gaussian. For cases of weak nonlinearity, the method is more accurate
than the linear method when both are compared to stochastic simulations.
