TY - JOUR
T1 - Multifidelity probability estimation via fusion of estimators
AU - Kramer, Boris
AU - Marques, Alexandre Noll
AU - Peherstorfer, Benjamin
AU - Villa, Umberto
AU - Willcox, Karen
N1 - Funding Information:
The authors thank Prof. M. Klein for sharing the DNS data in [39] with us. This work was supported by the Defense Advanced Research Projects Agency [EQUiPS program, award W911NF-15-2-0121 , Program Manager F. Fahroo]; the Air Force [Center of Excellence on Multi-Fidelity Modeling of Rocket Combustor Dynamics, award FA9550-17-1-0195 ]; and the US Department of Energy , Office of Advanced Scientific Computing Research (ASCR) [Applied Mathematics Program, awards DE-FG02-08ER2585 and DE-SC0009297 , as part of the DiaMonD Multifaceted Mathematics Integrated Capability Center].
Funding Information:
The authors thank Prof. M. Klein for sharing the DNS data in [39] with us. This work was supported by the Defense Advanced Research Projects Agency [EQUiPS program, award W911NF-15-2-0121, Program Manager F. Fahroo]; the Air Force [Center of Excellence on Multi-Fidelity Modeling of Rocket Combustor Dynamics, award FA9550-17-1-0195]; and the US Department of Energy, Office of Advanced Scientific Computing Research (ASCR) [Applied Mathematics Program, awards DE-FG02-08ER2585 and DE-SC0009297, as part of the DiaMonD Multifaceted Mathematics Integrated Capability Center].
Publisher Copyright:
© 2019 Elsevier Inc.
PY - 2019/9/1
Y1 - 2019/9/1
N2 - This paper develops a multifidelity method that enables estimation of failure probabilities for expensive-to-evaluate models via information fusion and importance sampling. The presented general fusion method combines multiple probability estimators with the goal of variance reduction. We use low-fidelity models to derive biasing densities for importance sampling and then fuse the importance sampling estimators such that the fused multifidelity estimator is unbiased and has mean-squared error lower than or equal to that of any of the importance sampling estimators alone. By fusing all available estimators, the method circumvents the challenging problem of selecting the best biasing density and using only that density for sampling. A rigorous analysis shows that the fused estimator is optimal in the sense that it has minimal variance amongst all possible combinations of the estimators. The asymptotic behavior of the proposed method is demonstrated on a convection-diffusion-reaction partial differential equation model for which 105 samples can be afforded. To illustrate the proposed method at scale, we consider a model of a free plane jet and quantify how uncertainties at the flow inlet propagate to a quantity of interest related to turbulent mixing. Compared to an importance sampling estimator that uses the high-fidelity model alone, our multifidelity estimator reduces the required CPU time by 65% while achieving a similar coefficient of variation.
AB - This paper develops a multifidelity method that enables estimation of failure probabilities for expensive-to-evaluate models via information fusion and importance sampling. The presented general fusion method combines multiple probability estimators with the goal of variance reduction. We use low-fidelity models to derive biasing densities for importance sampling and then fuse the importance sampling estimators such that the fused multifidelity estimator is unbiased and has mean-squared error lower than or equal to that of any of the importance sampling estimators alone. By fusing all available estimators, the method circumvents the challenging problem of selecting the best biasing density and using only that density for sampling. A rigorous analysis shows that the fused estimator is optimal in the sense that it has minimal variance amongst all possible combinations of the estimators. The asymptotic behavior of the proposed method is demonstrated on a convection-diffusion-reaction partial differential equation model for which 105 samples can be afforded. To illustrate the proposed method at scale, we consider a model of a free plane jet and quantify how uncertainties at the flow inlet propagate to a quantity of interest related to turbulent mixing. Compared to an importance sampling estimator that uses the high-fidelity model alone, our multifidelity estimator reduces the required CPU time by 65% while achieving a similar coefficient of variation.
KW - Failure probability estimation
KW - Information fusion
KW - Multifidelity modeling
KW - Reduced-order modeling
KW - Turbulent jet
KW - Uncertainty quantification
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U2 - 10.1016/j.jcp.2019.04.071
DO - 10.1016/j.jcp.2019.04.071
M3 - Article
AN - SCOPUS:85065442797
SN - 0021-9991
VL - 392
SP - 385
EP - 402
JO - Journal of Computational Physics
JF - Journal of Computational Physics
ER -