Multifidelity probability estimation via fusion of estimators

Boris Kramer, Alexandre Noll Marques, Benjamin Peherstorfer, Umberto Villa, Karen Willcox

Research output: Contribution to journalArticle

Abstract

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 10 5 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.

Original languageEnglish (US)
Pages (from-to)385-402
Number of pages18
JournalJournal of Computational Physics
Volume392
DOIs
StatePublished - Sep 1 2019

Fingerprint

Importance sampling
estimators
Fusion
fusion
Estimator
Importance Sampling
sampling
Inlet flow
Information fusion
Electric fuses
Fidelity
Partial differential equations
Program processors
Turbulent Mixing
inlet flow
Sampling
Variance Reduction
Model
turbulent mixing
Convection-diffusion

Keywords

  • Failure probability estimation
  • Information fusion
  • Multifidelity modeling
  • Reduced-order modeling
  • Turbulent jet
  • Uncertainty quantification

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

Cite this

Kramer, B., Marques, A. N., Peherstorfer, B., Villa, U., & Willcox, K. (2019). Multifidelity probability estimation via fusion of estimators. Journal of Computational Physics, 392, 385-402. https://doi.org/10.1016/j.jcp.2019.04.071

Multifidelity probability estimation via fusion of estimators. / Kramer, Boris; Marques, Alexandre Noll; Peherstorfer, Benjamin; Villa, Umberto; Willcox, Karen.

In: Journal of Computational Physics, Vol. 392, 01.09.2019, p. 385-402.

Research output: Contribution to journalArticle

Kramer, B, Marques, AN, Peherstorfer, B, Villa, U & Willcox, K 2019, 'Multifidelity probability estimation via fusion of estimators', Journal of Computational Physics, vol. 392, pp. 385-402. https://doi.org/10.1016/j.jcp.2019.04.071
Kramer, Boris ; Marques, Alexandre Noll ; Peherstorfer, Benjamin ; Villa, Umberto ; Willcox, Karen. / Multifidelity probability estimation via fusion of estimators. In: Journal of Computational Physics. 2019 ; Vol. 392. pp. 385-402.
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