Simulation of stochastic network dynamics via entropic matching

TL;DR

This paper introduces an improved approximation method for simulating complex stochastic network dynamics, using entropic matching to achieve better accuracy than traditional linear noise approximation while maintaining similar computational efficiency.

Contribution

The authors develop a novel entropic matching approach that minimizes Kullback-Leibler divergence to enhance stochastic network simulations beyond existing linear methods.

Findings

More accurate than linear noise approximation for weakly nonlinear systems

Retains computational complexity similar to standard methods

Effective in modeling coupled biomolecular processes

Abstract

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.