Efficiency of a micro-macro acceleration method for scale-separated stochastic differential equations
For researchers simulating multiscale stochastic systems, this work provides numerical evidence of the method's accuracy and efficiency, but it is an incremental study of an existing approach.
The paper numerically evaluates a micro-macro acceleration method for stiff SDEs with time-scale separation, showing it can take significantly larger time steps than the microscopic integrator while being more accurate than approximate macroscopic models.
We discuss through multiple numerical examples the accuracy and efficiency of a micro-macro acceleration method for stiff stochastic differential equations (SDEs) with a time-scale separation between the fast microscopic dynamics and the evolution of some slow macroscopic state variables. The algorithm interleaves a short simulation of the stiff SDE with extrapolation of the macroscopic state variables over a longer time interval. After extrapolation, we obtain the reconstructed microscopic state via a matching procedure: we compute the probability distribution that is consistent with the extrapolated state variables, while minimally altering the microscopic distribution that was available just before the extrapolation. In this work, we numerically study the accuracy and efficiency of micro-macro acceleration as a function of the extrapolation time step and as a function of the chosen macroscopic state variables. Additionally, we compare the effect of different hierarchies of macroscopic state variables. We illustrate that the method can take significantly larger time steps than the inner microscopic integrator, while simultaneously being more accurate than approximate macroscopic models.