Multi-scale control variate methods for uncertainty quantification in kinetic equations

TL;DR

This paper introduces multi-scale control variate methods to improve the efficiency of uncertainty quantification in kinetic equations, addressing high-dimensional challenges with variance reduction techniques.

Contribution

The paper develops novel multi-scale control variate methods that effectively reduce variance in Monte Carlo simulations for kinetic equations with uncertainties.

Findings

Significant variance reduction in Monte Carlo methods.

Enhanced computational efficiency for high-dimensional kinetic problems.

Applicable to systems with uncertain microscopic interactions.

Abstract

Kinetic equations play a major rule in modeling large systems of interacting particles. Uncertainties may be due to various reasons, like lack of knowledge on the microscopic interaction details or incomplete informations at the boundaries. These uncertainties, however, contribute to the curse of dimensionality and the development of efficient numerical methods is a challenge. In this paper we consider the construction of novel multi-scale methods for such problems which, thanks to a control variate approach, are capable to reduce the variance of standard Monte Carlo techniques.