Multi-level Monte Carlo acceleration of computations on multi-layer materials with random defects

TL;DR

This paper introduces a multi-level Monte Carlo method to efficiently compute properties of layered materials with random defects, significantly reducing computational time compared to standard Monte Carlo approaches.

Contribution

The paper develops a novel multi-level Monte Carlo technique tailored for materials with random defects, improving computational efficiency in property estimation.

Findings

Multi-level Monte Carlo reduces computational time substantially.

Effective for tight-binding models of graphene and MoS2.

Achieves desired accuracy with fewer simulations.

Abstract

We propose a Multi-level Monte Carlo technique to accelerate Monte Carlo sampling for approximation of properties of materials with random defects. The computational efficiency is investigated on test problems given by tight-binding models of a single layer of graphene or of $MoS_2$ where the integrated electron density of states per unit area is taken as a representative quantity of interest. For the chosen test problems the multi-level Monte Carlo estimators significantly reduce the computational time of standard Monte Carlo estimators to obtain a given accuracy.