Multilevel Monte Carlo for noise estimation in stochastic multiscale systems

Abstract

The purpose of this study is to adapt Multilevel Monte Carlo (MLMC) sampling technique for random noise estimation in stochastic multiscale systems and evaluate the performance of this method. The system under consideration was a simulation of thin film formation by chemical vapour deposition, where a kinetic Monte Carlo solid-on-solid model was coupled with partial differential equations that represented mass, energy and momentum transport. The noise in the expected value of the system�s observable (film roughness) was estimated using MLMC and standard Monte Carlo (MC) sampling. The MLMC technique achieved conservative estimates of noise in the observable at an order of magnitude lower computational cost than standard MC sampling. This study highlights the nuances of adapting the MLMC technique to the stochastic multiscale system and provides insight on the benefits and challenges of using MLMC for noise estimation in stochastic multiscale systems.