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A Multifidelity Monte Carlo Method for Realistic Computational Budgets

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Abstract

A method for the multifidelity Monte Carlo (MFMC) estimation of statistical quantities is proposed which is applicable to computational budgets of any size. Based on a sequence of optimization problems each with a globally minimizing closed-form solution, this method extends the usability of a well known MFMC algorithm, recovering it when the computational budget is large enough. Theoretical results verify that the proposed approach is at least as optimal as its namesake and retains the benefits of multifidelity estimation with minimal assumptions on the budget or amount of available data, providing a notable reduction in variance over simple Monte Carlo estimation.

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Data Availability

The datasets utilized during the current study were generated randomly with seed 2 according to the parameters in Algorithm 2 and the specifications in the text.

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Funding

This work is partially supported by U.S. Department of Energy under Grants DE-SC0020270, DE-SC0020418, and DE-SC0021077.

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Authors and Affiliations

  1. Department of Scientific Computing, Florida State University, 400 Dirac Science Library, Tallahassee, FL, 32306, USA

    Anthony Gruber & Max Gunzburger

  2. Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, 201 E 24th Street, Austin, TX, 78712, USA

    Max Gunzburger

  3. Department of Mathematics, University of South Carolina, 1523 Greene Street, Columbia, SC, 29208, USA

    Lili Ju & Zhu Wang

Authors
  1. Anthony Gruber
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  2. Max Gunzburger
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  3. Lili Ju
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  4. Zhu Wang
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Correspondence to Anthony Gruber.

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Gruber, A., Gunzburger, M., Ju, L. et al. A Multifidelity Monte Carlo Method for Realistic Computational Budgets. J Sci Comput 94, 2 (2023). https://doi.org/10.1007/s10915-022-02051-y

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  • DOI: https://doi.org/10.1007/s10915-022-02051-y

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