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Title: Utilizing Adjoint-Based Error Estimates for Surrogate Models to Accurately Predict Probabilities of Events

Abstract

In thist study, we develop a procedure to utilize error estimates for samples of a surrogate model to compute robust upper and lower bounds on estimates of probabilities of events. We show that these error estimates can also be used in an adaptive algorithm to simultaneously reduce the computational cost and increase the accuracy in estimating probabilities of events using computationally expensive high-fidelity models. Specifically, we introduce the notion of reliability of a sample of a surrogate model, and we prove that utilizing the surrogate model for the reliable samples and the high-fidelity model for the unreliable samples gives precisely the same estimate of the probability of the output event as would be obtained by evaluation of the original model for each sample. The adaptive algorithm uses the additional evaluations of the high-fidelity model for the unreliable samples to locally improve the surrogate model near the limit state, which significantly reduces the number of high-fidelity model evaluations as the limit state is resolved. Numerical results based on a recently developed adjoint-based approach for estimating the error in samples of a surrogate are provided to demonstrate (1) the robustness of the bounds on the probability of an event, and (2) thatmore » the adaptive enhancement algorithm provides a more accurate estimate of the probability of the QoI event than standard response surface approximation methods at a lower computational cost.« less

Authors:
 [1];  [2]
  1. Univ. of Colorado, Denver, CO (United States). Department of Mathematical and Statistical Sciences
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Optimization and Uncertainty Quantification Department
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
1429672
Report Number(s):
SAND-2017-11665J
Journal ID: ISSN 2152-5080; 658229
Grant/Contract Number:  
AC04-94AL85000; SC00009279
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
International Journal for Uncertainty Quantification
Additional Journal Information:
Journal Volume: 8; Journal Issue: 2; Journal ID: ISSN 2152-5080
Publisher:
Begell House
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; surrogate models; rare events; a posteriori error analysis; adjoint problem

Citation Formats

Butler, Troy, and Wildey, Timothy. Utilizing Adjoint-Based Error Estimates for Surrogate Models to Accurately Predict Probabilities of Events. United States: N. p., 2018. Web. doi:10.1615/Int.J.UncertaintyQuantification.2018020911.
Butler, Troy, & Wildey, Timothy. Utilizing Adjoint-Based Error Estimates for Surrogate Models to Accurately Predict Probabilities of Events. United States. doi:10.1615/Int.J.UncertaintyQuantification.2018020911.
Butler, Troy, and Wildey, Timothy. Mon . "Utilizing Adjoint-Based Error Estimates for Surrogate Models to Accurately Predict Probabilities of Events". United States. doi:10.1615/Int.J.UncertaintyQuantification.2018020911. https://www.osti.gov/servlets/purl/1429672.
@article{osti_1429672,
title = {Utilizing Adjoint-Based Error Estimates for Surrogate Models to Accurately Predict Probabilities of Events},
author = {Butler, Troy and Wildey, Timothy},
abstractNote = {In thist study, we develop a procedure to utilize error estimates for samples of a surrogate model to compute robust upper and lower bounds on estimates of probabilities of events. We show that these error estimates can also be used in an adaptive algorithm to simultaneously reduce the computational cost and increase the accuracy in estimating probabilities of events using computationally expensive high-fidelity models. Specifically, we introduce the notion of reliability of a sample of a surrogate model, and we prove that utilizing the surrogate model for the reliable samples and the high-fidelity model for the unreliable samples gives precisely the same estimate of the probability of the output event as would be obtained by evaluation of the original model for each sample. The adaptive algorithm uses the additional evaluations of the high-fidelity model for the unreliable samples to locally improve the surrogate model near the limit state, which significantly reduces the number of high-fidelity model evaluations as the limit state is resolved. Numerical results based on a recently developed adjoint-based approach for estimating the error in samples of a surrogate are provided to demonstrate (1) the robustness of the bounds on the probability of an event, and (2) that the adaptive enhancement algorithm provides a more accurate estimate of the probability of the QoI event than standard response surface approximation methods at a lower computational cost.},
doi = {10.1615/Int.J.UncertaintyQuantification.2018020911},
journal = {International Journal for Uncertainty Quantification},
issn = {2152-5080},
number = 2,
volume = 8,
place = {United States},
year = {2018},
month = {1}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Figures / Tables:

Figure 1: Figure 1:: Illustration of the utilization of the error bounds Css(λ)| to assess the reliability of a sample Js(λ). The surrogate sample Js1) is categorized as reliable since Css1)| smaller than the magnitudes of the difference between the surrogate and the limit state boundaries. The surrogate sample Js2)more » is categorized as unreliable since Css2)| indicates that the true quantity of interest value may be near the limit state even though Css1)| > Css2)|.« less

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