Multifidelity monte carlo estimation of variance and sensitivity indices

E. Qian, Benjamin Peherstorfer, D. O’Malley, V. V. Vesselinov, K. Willcox

Research output: Contribution to journalArticle

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 work 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× speedups for fixed convergence levels. For the problems tested, the multifidelity approach allows inputs to be definitively ranked in importance when Monte Carlo alone fails to do so.

Original languageEnglish (US)
Pages (from-to)683-706
Number of pages24
JournalSIAM-ASA Journal on Uncertainty Quantification
Volume6
Issue number2
DOIs
StatePublished - Jan 1 2018

Fingerprint

Sensitivity analysis
Sensitivity Analysis
Model
Uncertainty
Convection-diffusion
Leverage
Fidelity
Estimator
Resources
Output
Costs
Demonstrate
Strategy
Convection
Reaction-diffusion
Guarantee

Keywords

  • Global sensitivity analysis
  • Monte Carlo
  • Multifidelity

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

Qian, E., Peherstorfer, B., O’Malley, D., Vesselinov, V. V., & Willcox, K. (2018). Multifidelity monte carlo estimation of variance and sensitivity indices. SIAM-ASA Journal on Uncertainty Quantification, 6(2), 683-706. https://doi.org/10.1137/17M1151006

Multifidelity monte carlo estimation of variance and sensitivity indices. / Qian, E.; Peherstorfer, Benjamin; O’Malley, D.; Vesselinov, V. V.; Willcox, K.

In: SIAM-ASA Journal on Uncertainty Quantification, Vol. 6, No. 2, 01.01.2018, p. 683-706.

Research output: Contribution to journalArticle

Qian, E, Peherstorfer, B, O’Malley, D, Vesselinov, VV & Willcox, K 2018, 'Multifidelity monte carlo estimation of variance and sensitivity indices', SIAM-ASA Journal on Uncertainty Quantification, vol. 6, no. 2, pp. 683-706. https://doi.org/10.1137/17M1151006
Qian, E. ; Peherstorfer, Benjamin ; O’Malley, D. ; Vesselinov, V. V. ; Willcox, K. / Multifidelity monte carlo estimation of variance and sensitivity indices. In: SIAM-ASA Journal on Uncertainty Quantification. 2018 ; Vol. 6, No. 2. pp. 683-706.
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