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Title: Multifidelity Monte Carlo Estimation of Variance and Sensitivity Indices

Journal Article · · SIAM/ASA Journal on Uncertainty Quantification
DOI:https://doi.org/10.1137/17M1151006· OSTI ID:1480021
 [1];  [2];  [3];  [3];  [1]
  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)
+ Show Author Affiliations

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.

Research Organization:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
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)
Grant/Contract Number:
AC52-06NA25396; FG02-08ER25858; SC0009297; FA9550-17-1-0195
OSTI ID:
1480021
Report Number(s):
LA-UR-17-29565
Journal Information:
SIAM/ASA Journal on Uncertainty Quantification, Vol. 6, Issue 2; ISSN 2166-2525
Publisher:
SIAMCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 26 works
Citation information provided by
Web of Science

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Cited By (2)

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

Figures / Tables (17)

Table 1(p. 11)table Table 1
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Table 2(p. 12)table Table 2
Table 3(p. 13)table Table 3
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Table 4(p. 18)table Table 4
Table 5(p. 19)table Table 5
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Figure 11(p. 26)figure Figure 11
Figure 12(p. 27)figure Figure 12

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97 MATHEMATICS AND COMPUTING
Mathematics