Utilizing AdjointBased 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 highfidelity 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 highfidelity 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 highfidelity model for the unreliable samples to locally improve the surrogate model near the limit state, which significantly reduces the number of highfidelity model evaluations as the limit state is resolved. Numerical results based on a recently developed adjointbased 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 »
 Authors:

 Univ. of Colorado, Denver, CO (United States). Department of Mathematical and Statistical Sciences
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States). Optimization and Uncertainty Quantification Department
 Publication Date:
 Research Org.:
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC21)
 OSTI Identifier:
 1429672
 Report Number(s):
 SAND201711665J
Journal ID: ISSN 21525080; 658229
 Grant/Contract Number:
 AC0494AL85000; 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 21525080
 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 AdjointBased 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 AdjointBased 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 AdjointBased 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 AdjointBased 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 highfidelity 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 highfidelity 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 highfidelity model for the unreliable samples to locally improve the surrogate model near the limit state, which significantly reduces the number of highfidelity model evaluations as the limit state is resolved. Numerical results based on a recently developed adjointbased 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 = {21525080},
number = 2,
volume = 8,
place = {United States},
year = {2018},
month = {1}
}