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Link to original content: https://doi.org/10.48550/arXiv.2206.07572
[2206.07572] A Multifidelity Monte Carlo Method for Realistic Computational Budgets
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Mathematics > Numerical Analysis

arXiv:2206.07572 (math)
[Submitted on 15 Jun 2022 (v1), last revised 13 Nov 2022 (this version, v2)]

Title:A Multifidelity Monte Carlo Method for Realistic Computational Budgets

Authors:Anthony Gruber, Max Gunzburger, Lili Ju, Zhu Wang
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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.
Subjects: Numerical Analysis (math.NA); Optimization and Control (math.OC)
MSC classes: 62K05, 49M20
Cite as: arXiv:2206.07572 [math.NA]
  (or arXiv:2206.07572v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2206.07572

Submission history

From: Anthony Gruber [view email]
[v1] Wed, 15 Jun 2022 14:49:11 UTC (1,880 KB)
[v2] Sun, 13 Nov 2022 02:16:04 UTC (4,509 KB)
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