RT Journal Article ID 288aec6a51c2bb8f A1 Butler, Troy A1 Wildey, Timothy T1 UTILIZING ADJOINT-BASED ERROR ESTIMATES FOR SURROGATE MODELS TO ACCURATELY PREDICT PROBABILITIES OF EVENTS JF International Journal for Uncertainty Quantification JO IJUQ YR 2018 FD 2018-04-03 VO 8 IS 2 SP 143 OP 159 K1 surrogate models K1 rare events K1 a posteriori error analysis K1 adjoint problem AB 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. PB Begell House LK https://www.dl.begellhouse.com/journals/52034eb04b657aea,17c65e9d6874abc6,288aec6a51c2bb8f.html