Projective integration of expensive multiscale stochastic simulation

Abstract

Consider the case when a microscale simulator is too expensive for long time simulations necessary to determine macroscale dynamics. Projective integration uses bursts of the microscale simulator, using microscale time steps, and computes an approximation to the system over a macroscale time step by extrapolation. Projective integration has the potential to be an effective method to compute the long time dynamic behaviour of multiscale systems. However, many multiscale systems are influenced by noise. Thus it is important to consider the projective integration of such systems. By the maximum likelihood estimation, we estimate a linear stochastic differential equation from short bursts of data. The analytic solution of the linear stochastic differential equation then estimates the solution over a macroscale time step. We explore how the noise affects the projective integration in different methods. Monte Carlo simulation suggests design parameters offering stability and accuracy for the algorithms. The algorithms developed here may be applied to compute the long time dynamic behaviour of multiscale systems with noise.