Convergence analysis of multifidelity Monte Carlo estimation

Benjamin Peherstorfer, Max Gunzburger, Karen Willcox

Research output: Contribution to journalArticle

Abstract

The multifidelity Monte Carlo method provides a general framework for combining cheap low-fidelity approximations of an expensive high-fidelity model to accelerate the Monte Carlo estimation of statistics of the high-fidelity model output. In this work, we investigate the properties of multifidelity Monte Carlo estimation in the setting where a hierarchy of approximations can be constructed with known error and cost bounds. Our main result is a convergence analysis of multifidelity Monte Carlo estimation, for which we prove a bound on the costs of the multifidelity Monte Carlo estimator under assumptions on the error and cost bounds of the low-fidelity approximations. The assumptions that we make are typical in the setting of similar Monte Carlo techniques. Numerical experiments illustrate the derived bounds.

Original languageEnglish (US)
Pages (from-to)683-707
Number of pages25
JournalNumerische Mathematik
Volume139
Issue number3
DOIs
StatePublished - Jul 1 2018

Fingerprint

Convergence Analysis
Fidelity
Costs
Approximation
Monte Carlo Techniques
Monte Carlo methods
Statistics
Monte Carlo method
Accelerate
Numerical Experiment
Estimator
Output
Experiments
Model

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this

Convergence analysis of multifidelity Monte Carlo estimation. / Peherstorfer, Benjamin; Gunzburger, Max; Willcox, Karen.

In: Numerische Mathematik, Vol. 139, No. 3, 01.07.2018, p. 683-707.

Research output: Contribution to journalArticle

Peherstorfer, B, Gunzburger, M & Willcox, K 2018, 'Convergence analysis of multifidelity Monte Carlo estimation', Numerische Mathematik, vol. 139, no. 3, pp. 683-707. https://doi.org/10.1007/s00211-018-0945-7
Peherstorfer, Benjamin ; Gunzburger, Max ; Willcox, Karen. / Convergence analysis of multifidelity Monte Carlo estimation. In: Numerische Mathematik. 2018 ; Vol. 139, No. 3. pp. 683-707.
@article{2994fb95a6d04cffafb445cdb0b71a42,
title = "Convergence analysis of multifidelity Monte Carlo estimation",
abstract = "The multifidelity Monte Carlo method provides a general framework for combining cheap low-fidelity approximations of an expensive high-fidelity model to accelerate the Monte Carlo estimation of statistics of the high-fidelity model output. In this work, we investigate the properties of multifidelity Monte Carlo estimation in the setting where a hierarchy of approximations can be constructed with known error and cost bounds. Our main result is a convergence analysis of multifidelity Monte Carlo estimation, for which we prove a bound on the costs of the multifidelity Monte Carlo estimator under assumptions on the error and cost bounds of the low-fidelity approximations. The assumptions that we make are typical in the setting of similar Monte Carlo techniques. Numerical experiments illustrate the derived bounds.",
author = "Benjamin Peherstorfer and Max Gunzburger and Karen Willcox",
year = "2018",
month = "7",
day = "1",
doi = "10.1007/s00211-018-0945-7",
language = "English (US)",
volume = "139",
pages = "683--707",
journal = "Numerische Mathematik",
issn = "0029-599X",
publisher = "Springer New York",
number = "3",

}

TY - JOUR

T1 - Convergence analysis of multifidelity Monte Carlo estimation

AU - Peherstorfer, Benjamin

AU - Gunzburger, Max

AU - Willcox, Karen

PY - 2018/7/1

Y1 - 2018/7/1

N2 - The multifidelity Monte Carlo method provides a general framework for combining cheap low-fidelity approximations of an expensive high-fidelity model to accelerate the Monte Carlo estimation of statistics of the high-fidelity model output. In this work, we investigate the properties of multifidelity Monte Carlo estimation in the setting where a hierarchy of approximations can be constructed with known error and cost bounds. Our main result is a convergence analysis of multifidelity Monte Carlo estimation, for which we prove a bound on the costs of the multifidelity Monte Carlo estimator under assumptions on the error and cost bounds of the low-fidelity approximations. The assumptions that we make are typical in the setting of similar Monte Carlo techniques. Numerical experiments illustrate the derived bounds.

AB - The multifidelity Monte Carlo method provides a general framework for combining cheap low-fidelity approximations of an expensive high-fidelity model to accelerate the Monte Carlo estimation of statistics of the high-fidelity model output. In this work, we investigate the properties of multifidelity Monte Carlo estimation in the setting where a hierarchy of approximations can be constructed with known error and cost bounds. Our main result is a convergence analysis of multifidelity Monte Carlo estimation, for which we prove a bound on the costs of the multifidelity Monte Carlo estimator under assumptions on the error and cost bounds of the low-fidelity approximations. The assumptions that we make are typical in the setting of similar Monte Carlo techniques. Numerical experiments illustrate the derived bounds.

UR - http://www.scopus.com/inward/record.url?scp=85040690135&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85040690135&partnerID=8YFLogxK

U2 - 10.1007/s00211-018-0945-7

DO - 10.1007/s00211-018-0945-7

M3 - Article

AN - SCOPUS:85040690135

VL - 139

SP - 683

EP - 707

JO - Numerische Mathematik

JF - Numerische Mathematik

SN - 0029-599X

IS - 3

ER -