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Analysis of the Challenges in Developing Sample-Based Multi-fidelity Estimators for Non-deterministic Models

Journal Article · · International Journal for Uncertainty Quantification
 [1];  [1];  [1]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

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. Here, 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.

Research Organization:
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC)
Grant/Contract Number:
NA0003525
OSTI ID:
2351026
Report Number(s):
SAND--2024-06279J
Journal Information:
International Journal for Uncertainty Quantification, Journal Name: International Journal for Uncertainty Quantification Journal Issue: 5 Vol. 14; ISSN 2152-5080
Publisher:
Begell HouseCopyright Statement
Country of Publication:
United States
Language:
English

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