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

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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