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Title: Multifidelity Monte Carlo Estimation of Variance and Sensitivity Indices

Abstract

Variance-based 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 low-fidelity 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 convection-diffusion-reaction 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:
 [1];  [2];  [3];  [3];  [1]
+ Show Author Affiliations
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Aeronautics and Astronautics
  2. Univ. of Wisconsin, Madison, WI (United States). Dept. of Mechanical Engineering
  3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF); Fannie and John Hertz Foundation (United States); US Air Force Office of Scientific Research (AFOSR)
OSTI Identifier:
1480021
Report Number(s):
LA-UR-17-29565
Journal ID: ISSN 2166-2525
Grant/Contract Number:  
AC52-06NA25396; FG02-08ER25858; SC0009297; FA9550-17-1-0195
Resource Type:
Accepted Manuscript
Journal Name:
SIAM/ASA Journal on Uncertainty Quantification
Additional Journal Information:
Journal Volume: 6; Journal Issue: 2; Journal ID: ISSN 2166-2525
Publisher:
SIAM
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Mathematics

Citation Formats

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., 2018. Web. doi:10.1137/17M1151006.
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Qian, E., Peherstorfer, B., O'Malley, D., Vesselinov, V. V., & Willcox, K. Multifidelity Monte Carlo Estimation of Variance and Sensitivity Indices. United States. https://doi.org/10.1137/17M1151006
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Qian, E., Peherstorfer, B., O'Malley, D., Vesselinov, V. V., and Willcox, K. Tue . "Multifidelity Monte Carlo Estimation of Variance and Sensitivity Indices". United States. https://doi.org/10.1137/17M1151006. https://www.osti.gov/servlets/purl/1480021.
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@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 = {Variance-based 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 low-fidelity 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 convection-diffusion-reaction 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 = {Tue May 15 00:00:00 EDT 2018},
month = {Tue May 15 00:00:00 EDT 2018}
}
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Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1137/17M1151006
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Citation Metrics:
Cited by: 26 works
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Figures / Tables:

Table 1 Table 1: Main and total effect sensitivity indices for Ishigami function with constants $a$ = 5, $b$ = 0.1.
All figures and tables (17 total)
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    Works referencing / citing this record:

    A transport-based multifidelity preconditioner for Markov chain Monte Carlo
    journal, November 2019

    A transport-based multifidelity preconditioner for Markov chain Monte Carlo
    preprint, January 2018

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      Figures / Tables found in this record:

      Table 1 (p. 11)table
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