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International Journal for Uncertainty Quantification
Factor de Impacto: 4.911 Factor de Impacto de 5 años: 3.179 SJR: 1.008 SNIP: 0.983 CiteScore™: 5.2

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

Acceso abierto

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2019026974
pages 415-437


Timothy Wildey
Optimization and Uncertainty Quantification Department, Center for Computing Research, Sandia National Laboratories, Albuquerque, NM 87185
A. A. Gorodetsky
University of Michigan, Department of Aerospace Engineering, Ann Arbor, MI 48109
A. Belme
Sorbonne Universités, UPMC Univ Paris 06, UMR 7190, Institut Jean le Rond d'Alembert, F-75005, Paris, France; CNRS, UMR 7190, Institut Jean le Rond d'Alembert, F-75005, Paris, France
John N. Shadid
Computational Mathematics Department, Center for Computing Research, Sandia National Laboratories, Albuquerque, NM 87185, and Department of Mathematics and Statistics, University of New Mexico


This paper considers response surface approximations for discontinuous quantities of interest. Our objective is not to adaptively characterize the interface defining the discontinuity. Instead, we utilize an epistemic description of the uncertainty in the location of a discontinuity to produce robust bounds on sample-based estimates of probabilistic quantities of interest. We demonstrate that two common machine learning strategies for classification, one based on nearest neighbors (Voronoi cells) and one based on support vector machines, provide reasonable descriptions of the region where the discontinuity may reside. In higher dimensional spaces, we demonstrate that support vector machines are more accurate for discontinuities defined by smooth interfaces. We also show how gradient information, often available via adjoint-based approaches, can be used to define indicators to effectively detect a discontinuity and to decompose the samples into clusters using an unsupervised learning technique. Numerical results demonstrate the epistemic bounds on probabilistic quantities of interest for simplistic models and for a compressible fluid model with a shock-induced discontinuity.


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