Suscripción a Biblioteca: Guest
Portal Digitalde Biblioteca Digital eLibros Revistas Referencias y Libros de Ponencias Colecciones
International Journal for Uncertainty Quantification
Factor de Impacto: 3.259 Factor de Impacto de 5 años: 2.547 SJR: 0.417 SNIP: 0.8 CiteScore™: 1.52

ISSN Imprimir: 2152-5080
ISSN En Línea: 2152-5099

Acceso abierto

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2018020911
pages 143-159

UTILIZING ADJOINT-BASED ERROR ESTIMATES FOR SURROGATE MODELS TO ACCURATELY PREDICT PROBABILITIES OF EVENTS

Troy Butler
Department of Mathematical and Statistical Sciences, University of Colorado Denver, Colorado 80217, USA
Timothy Wildey
Optimization and Uncertainty Quantification Department, Center for Computing Research, Sandia National Laboratories, Albuquerque, NM 87185

SINOPSIS

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.


Articles with similar content:

AN ADAPTIVE REDUCED-DIMENSIONAL DISCRETE ELEMENT MODEL FOR DYNAMIC RESPONSES OF GRANULAR MATERIALS WITH HIGH-FREQUENCY NOISES
International Journal for Multiscale Computational Engineering, Vol.16, 2018, issue 4
WaiChing Sun, Xinran Zhong
BAYESIAN APPROACH TO THE STATISTICAL INVERSE PROBLEM OF SCATTEROMETRY: COMPARISON OF THREE SURROGATE MODELS
International Journal for Uncertainty Quantification, Vol.5, 2015, issue 6
Markus Bar, Sebastian Heidenreich, Hermann Gross
PRIOR AND POSTERIOR ROBUST STOCHASTIC PREDICTIONS FOR DYNAMICAL SYSTEMS USING PROBABILITY LOGIC
International Journal for Uncertainty Quantification, Vol.3, 2013, issue 4
Alexandros Taflanidis, James L. Beck
Order Reduction for Large-Scale Finite Element Models: A Systems Perspective
International Journal for Multiscale Computational Engineering, Vol.3, 2005, issue 3
William Gressick, John T. Wen, Jacob Fish
HESSIAN-BASED SAMPLING FOR HIGH-DIMENSIONAL MODEL REDUCTION
International Journal for Uncertainty Quantification, Vol.9, 2019, issue 2
Omar Ghattas, Peng Chen