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Numerische Mathematik

, Volume 139, Issue 3, pp 683–707 | Cite as

Convergence analysis of multifidelity Monte Carlo estimation

  • Benjamin PeherstorferEmail author
  • Max Gunzburger
  • Karen Willcox
Article

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.

Mathematics Subject Classification

35Q62 65C05 60H35 35R60 65N15 

Notes

Acknowledgements

The first and the third author were supported in part by the AFOSR MURI on multi-information sources of multi-physics systems under Award Number FA9550-15-1-0038, program manager Jean-Luc Cambier, and by the United States Department of Energy Applied Mathematics Program, Awards DE-FG02-08ER2585 and DE-SC0009297, as part of the DiaMonD Multifaceted Mathematics Integrated Capability Center. The second author was supported by the US Department of Energy Office of Science grant DE-SC0009324 and the Air Force Office of Scientific Grant FA9550-15-1-0001. Some of the numerical examples were computed on the computer cluster of the Munich Centre of Advanced Computing.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Benjamin Peherstorfer
    • 1
    Email author
  • Max Gunzburger
    • 2
  • Karen Willcox
    • 3
  1. 1.Department of Mechanical Engineering and Wisconsin Institute for DiscoveryUniversity of Wisconsin-MadisonMadisonUSA
  2. 2.Department of Scientific ComputingFlorida State UniversityTallahasseeUSA
  3. 3.Department of Aeronautics and AstronauticsMITCambridgeUSA

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