(315e) Multilevel Monte Carlo Applied for Efficient Estimation of Observables in Multiscale Stochastic Systems
AIChE Annual Meeting
Tuesday, October 30, 2018 - 1:46pm to 2:05pm
In our previous work, we applied MLMC to uncertainty quantification in classic chemical engineering systems . In this work, we extend and adapt MLMC to perform accurate estimation of observables in stochastic multiscale systems. We used as a case study a model of thin film formation by Chemical Vapour Deposition (CVD) , which was also previously used to quantify uncertainty and estimation of observables in multiscale systems ,. In this model, a kinetic Monte Carlo (kMC) solid-on-solid simulation represents the microscale formation of a thin film, while continuum mass, energy and momentum transfer equations are used to represent the macroscale supply of the chemical vapor to the substrate where the film forms. The non-closed-form microscale representation and the deterministic macroscale equations are coupled through a boundary condition and thus form a stochastic multiscale system.
Most of the studies that use MLMC, including our previous work , discretize the time domain of continuous equations and use finer discretization for higher levels of approximation accuracy. In the CVD system, the accuracy of approximation increases with larger lattice sizes of the kMC simulation. We established an empirical relationship that relates the kMC time step to the lattice size and used it to control the definition of higher accuracy levels in the MLMC framework. We demonstrate that MLMC can be used to accurately estimate the observables of this multiscale stochastic system in a fraction of the time required when conducting the conventional Monte Carlo sampling of the full multiscale simulation.
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