Convergence analysis of multifidelity Monte Carlo estimation
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211_2018_945_ReferencePDF.pdf
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Author(s)
Peherstorfer, Benjamin
Gunzburger, Max
Willcox, Karen
Date Issued
January 19, 2018
Publisher
Springer Berlin Heidelberg
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
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DOI of Published Version
https://doi.org/10.1007/s00211-018-0945-7
