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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| Vydané v: | Computer methods in applied mechanics and engineering Ročník 413; číslo C; s. 116130 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
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United States
Elsevier B.V
01.08.2023
Elsevier |
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| ISSN: | 0045-7825, 1879-2138 |
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| Abstract | 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. |
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| AbstractList | 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. 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. Here, we demonstrate the efficacy of the new methods and formulations in practical UQ problems with model heterogeneity. |
| ArticleNumber | 116130 |
| Author | Willcox, K.E. Croci, M. Wright, S.J. |
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| BackLink | https://www.osti.gov/servlets/purl/2417967$$D View this record in Osti.gov |
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| Cites_doi | 10.1016/0025-5564(67)90026-0 10.1007/s00791-011-0160-x 10.1137/18M1175239 10.1137/20M1329044 10.1002/nme.4761 10.1007/s00211-015-0734-5 10.1137/0117110 10.1137/20M1321607 10.1007/BF02777575 10.1017/S096249291500001X 10.1137/1038003 10.1007/s10107-004-0559-y 10.1137/15M1046472 10.1007/s10107-002-0339-5 10.1016/j.jcp.2020.109257 10.1137/19M1263534 10.1287/opre.1070.0496 10.1111/j.1467-9868.2011.00777.x 10.1007/s10107-002-0347-5 10.1137/16M1082469 10.1137/0117041 |
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| SubjectTerms | Engineering Mathematics MATHEMATICS AND COMPUTING Mechanics Model selection Multifidelity Monte Carlo Multilevel Monte Carlo Sample allocation Semidefinite programming Uncertainty quantification |
| Title | Multi-output multilevel best linear unbiased estimators via semidefinite programming |
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