Multi-output multilevel best linear unbiased estimators via semidefinite programming

Multifidelity forward uncertainty quantification (UQ) problems often involve multiple quantities of interest and heterogeneous models (e.g., different grids, equations, dimensions, physics, surrogate and reduced-order models). While computational efficiency is key in this context, multi-output strat...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering Vol. 413; no. C; p. 116130
Main Authors: Croci, M., Willcox, K.E., Wright, S.J.
Format: Journal Article
Language:English
Published: United States Elsevier B.V 01.08.2023
Elsevier
Subjects:
Engineering
Mathematics
MATHEMATICS AND COMPUTING
Mechanics
Model selection
Multifidelity Monte Carlo
Multilevel Monte Carlo
Sample allocation
Semidefinite programming
Uncertainty quantification
Multilevel Monte Carlo
Uncertainty quantification
Semidefinite programming
Multifidelity Monte Carlo
Sample allocation
Model selection
ISSN:0045-7825, 1879-2138
Online Access:Get full text
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Summary:Multifidelity forward uncertainty quantification (UQ) problems often involve multiple quantities of interest and heterogeneous models (e.g., different grids, equations, dimensions, physics, surrogate and reduced-order models). While computational efficiency is key in this context, multi-output strategies in multilevel/multifidelity methods are either sub-optimal or non-existent. In this paper we extend multilevel best linear unbiased estimators (MLBLUE) to multi-output forward UQ problems and we present new semidefinite programming formulations for their optimal setup. Not only do these formulations yield the optimal number of samples required, but also the optimal selection of low-fidelity models to use. While existing MLBLUE approaches are single-output only and require a non-trivial nonlinear optimization procedure, the new multi-output formulations can be solved reliably and efficiently. We demonstrate the efficacy of the new methods and formulations in practical UQ problems with model heterogeneity.
Bibliography:National Science Foundation (NSF)
NA0003969; 8F-30039; FA9550-21-1-0084; DMS 2023239; CCF 2224213
USDOE National Nuclear Security Administration (NNSA)
US Air Force Office of Scientific Research (AFOSR)
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2023.116130