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 »
- Authors:
-
- Univ. of Colorado, Denver, CO (United States). Department of Mathematical and Statistical Sciences
- 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}
}
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Figure 1:: Illustration of the utilization of the error bounds Cs |ϵs(λ)| to assess the reliability of a sample Js(λ). The surrogate sample Js(λ1) is categorized as reliable since Cs |ϵs(λ1)| smaller than the magnitudes of the difference between the surrogate and the limit state boundaries. The surrogate sample Js(λ2)more »