Multifidelity Monte Carlo Estimation of Variance and Sensitivity Indices
Variancebased sensitivity analysis provides a quantitative measure of how uncertainty in a model input contributes to uncertainty in the model output. Such sensitivity analyses arise in a wide variety of applications and are typically computed using Monte Carlo estimation, but the many samples required for Monte Carlo to be sufficiently accurate can make these analyses intractable when the model is expensive. This paper presents a multifidelity approach for estimating sensitivity indices that leverages cheaper lowfidelity models to reduce the cost of sensitivity analysis while retaining accuracy guarantees via recourse to the original, expensive model. This paper develops new multifidelity estimators for variance and for the Sobol' main and total effect sensitivity indices. We discuss strategies for dividing limited computational resources among models and specify a recommended strategy. Results are presented for the Ishigami function and a convectiondiffusionreaction model that demonstrate up to $$10\times$$ speedups for fixed convergence levels. Finally, for the problems tested, the multifidelity approach allows inputs to be definitively ranked in importance when Monte Carlo alone fails to do so.
 Authors:

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 Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Aeronautics and Astronautics
 Univ. of Wisconsin, Madison, WI (United States). Dept. of Mechanical Engineering
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Report Number(s):
 LAUR1729565
Journal ID: ISSN 21662525
 Grant/Contract Number:
 AC5206NA25396; FG0208ER25858; SC0009297; FA95501710195
 Type:
 Accepted Manuscript
 Journal Name:
 SIAM/ASA Journal on Uncertainty Quantification
 Additional Journal Information:
 Journal Volume: 6; Journal Issue: 2; Journal ID: ISSN 21662525
 Publisher:
 SIAM
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC21); National Science Foundation (NSF); Fannie and John Hertz Foundation (United States); US Air Force Office of Scientific Research (AFOSR)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Mathematics
 OSTI Identifier:
 1480021
Qian, E., Peherstorfer, B., O'Malley, D., Vesselinov, V. V., and Willcox, K.. Multifidelity Monte Carlo Estimation of Variance and Sensitivity Indices. United States: N. p.,
Web. doi:10.1137/17M1151006.
Qian, E., Peherstorfer, B., O'Malley, D., Vesselinov, V. V., & Willcox, K.. Multifidelity Monte Carlo Estimation of Variance and Sensitivity Indices. United States. doi:10.1137/17M1151006.
Qian, E., Peherstorfer, B., O'Malley, D., Vesselinov, V. V., and Willcox, K.. 2018.
"Multifidelity Monte Carlo Estimation of Variance and Sensitivity Indices". United States.
doi:10.1137/17M1151006.
@article{osti_1480021,
title = {Multifidelity Monte Carlo Estimation of Variance and Sensitivity Indices},
author = {Qian, E. and Peherstorfer, B. and O'Malley, D. and Vesselinov, V. V. and Willcox, K.},
abstractNote = {Variancebased sensitivity analysis provides a quantitative measure of how uncertainty in a model input contributes to uncertainty in the model output. Such sensitivity analyses arise in a wide variety of applications and are typically computed using Monte Carlo estimation, but the many samples required for Monte Carlo to be sufficiently accurate can make these analyses intractable when the model is expensive. This paper presents a multifidelity approach for estimating sensitivity indices that leverages cheaper lowfidelity models to reduce the cost of sensitivity analysis while retaining accuracy guarantees via recourse to the original, expensive model. This paper develops new multifidelity estimators for variance and for the Sobol' main and total effect sensitivity indices. We discuss strategies for dividing limited computational resources among models and specify a recommended strategy. Results are presented for the Ishigami function and a convectiondiffusionreaction model that demonstrate up to $10\times$ speedups for fixed convergence levels. Finally, for the problems tested, the multifidelity approach allows inputs to be definitively ranked in importance when Monte Carlo alone fails to do so.},
doi = {10.1137/17M1151006},
journal = {SIAM/ASA Journal on Uncertainty Quantification},
number = 2,
volume = 6,
place = {United States},
year = {2018},
month = {5}
}