ANALYSIS OF THE CHALLENGES IN DEVELOPING SAMPLE-BASED MULTIFIDELITY ESTIMATORS FOR NONDETERMINISTIC MODELS
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Published:2024
Issue:5
Volume:14
Page:1-30
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ISSN:2152-5080
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Container-title:International Journal for Uncertainty Quantification
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language:en
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Short-container-title:Int. J. UncertaintyQuantification
Author:
Reuter Bryan W.,Geraci Gianluca,Wildey Timothy
Abstract
Multifidelity (MF) uncertainty quantification (UQ) seeks to leverage and fuse information from a collection of models
to achieve greater statistical accuracy with respect to a single-fidelity counterpart, while maintaining an efficient use of computational resources. Despite many recent advancements in MF UQ, several challenges remain and these often limit its practical impact in certain application areas. In this manuscript, we focus on the challenges introduced by nondeterministic models to sampling MF UQ estimators. Nondeterministic models produce different responses for the same inputs, which means their outputs are effectively noisy. MF UQ is complicated by this noise since many state-of-the-art approaches rely on statistics, e.g., the correlation among models, to optimally fuse information and allocate computational resources. We demonstrate how the statistics of the quantities of interest, which impact the
design, effectiveness, and use of existing MF UQ techniques, change as functions of the noise. With this in hand, we
extend the unifying approximate control variate framework to account for nondeterminism, providing for the first time
a rigorous means of comparing the effect of nondeterminism on different multifidelity estimators and analyzing their
performance with respect to one another. Numerical examples are presented throughout the manuscript to illustrate
and discuss the consequences of the presented theoretical results.
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