# Multi-scale variance reduction methods based on multiple control variates for kinetic equations with uncertainties

## TL;DR

This paper introduces a generalized multiscale control variate approach with multiple variates to significantly enhance variance reduction in Monte Carlo methods for kinetic equations with uncertainties, addressing high-dimensional challenges.

## Contribution

The paper extends previous multiscale control variate methods by incorporating multiple control variates, improving variance reduction for stochastic kinetic equations.

## Key findings

- Enhanced variance reduction with multiple control variates.
- Significant acceleration of Monte Carlo convergence.
- Effective handling of high-dimensional stochastic problems.

## Abstract

The development of efficient numerical methods for kinetic equations with stochastic parameters is a challenge due to the high dimensionality of the problem. Recently we introduced a multiscale control variate strategy which is capable to accelerate considerably the slow convergence of standard Monte Carlo methods for uncertainty quantification. Here we generalize this class of methods to the case of multiple control variates. We show that the additional degrees of freedom can be used to improve further the variance reduction properties of multiscale control variate methods.