MULTISCALE VARIANCE REDUCTION METHODS BASED ON MULTIPLE CONTROL VARIATES FOR KINETIC EQUATIONS WITH UNCERTAINTIES

被引：14

作者：

Dimarco, Giacomo ^{[1
]}

Pareschi, Lorenzo ^{[1
]}

机构：

[1] Univ Ferrara, Dept Math & Comp Sci, Via Machiavelli 30, I-44121 Ferrara, Italy

来源：

MULTISCALE MODELING & SIMULATION | 2020年 / 18卷 / 01期

关键词：

uncertainty quantification; kinetic equations; Monte Carlo methods; multiple control variates; multiscale methods; multifidelity methods; STOCHASTIC COLLOCATION METHOD; BOLTZMANN-EQUATION; GALERKIN METHOD; CONVERGENCE; QUANTIFICATION; EQUILIBRIUM; BOUNDS; MODEL;

D O I：

10.1137/18M1231985

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 of considerably accelerating 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 further improve the variance reduction properties of multiscale control variate methods.

引用

页码：351 / 382

页数：32

共 42 条

[1] Uncertainty Quantification in Control Problems for Flocking Models [J].