Robust Uncertainty Quantification using Response Surface Approximations of Discontinuous Functions

Wildey, Timothy Michael; Gorodetsky, Alex; Belme, Anca; Shadid, John N.

doi:10.1615/Int.J.UncertaintyQuantification.2019026974

Title: Robust Uncertainty Quantification using Response Surface Approximations of Discontinuous Functions

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Abstract

This paper considers response surface approximations for discontinuous quantities of interest. Our objective is not to adaptively characterize the manifold 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 manifolds. 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.

Authors:

Wildey, Timothy Michael ^[1]; Gorodetsky, Alex ^[2]; Belme, Anca ^[3]; Shadid, John N. ^[4]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Univ. of Michigan, Ann Arbor, MI (United States)
Sorbonne Univ., Paris (France)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Univ. of New Mexico, Albuquerque, NM (United States)

Publication Date:: Tue Jan 01 00:00:00 EST 2019

Research Org.:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1559480

Report Number(s):: SAND-2019-4016J
Journal ID: ISSN 2152-5080; 674563

Grant/Contract Number:: AC04-94AL85000

Resource Type:: Accepted Manuscript

Journal Name:: International Journal for Uncertainty Quantification

Additional Journal Information:: Journal Volume: 9; Journal Issue: 5; Journal ID: ISSN 2152-5080

Publisher:: Begell House

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING

Citation Formats


                    Wildey, Timothy Michael, Gorodetsky, Alex, Belme, Anca, and Shadid, John N. Robust Uncertainty Quantification using Response Surface Approximations of Discontinuous Functions.  United States: N. p., 2019. 
Web.  doi:10.1615/Int.J.UncertaintyQuantification.2019026974.

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                    Wildey, Timothy Michael, Gorodetsky, Alex, Belme, Anca, & Shadid, John N. Robust Uncertainty Quantification using Response Surface Approximations of Discontinuous Functions.  United States.  https://doi.org/10.1615/Int.J.UncertaintyQuantification.2019026974

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                    Wildey, Timothy Michael, Gorodetsky, Alex, Belme, Anca, and Shadid, John N. Tue .  
"Robust Uncertainty Quantification using Response Surface Approximations of Discontinuous Functions".  United States.  https://doi.org/10.1615/Int.J.UncertaintyQuantification.2019026974.  https://www.osti.gov/servlets/purl/1559480.

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@article{osti_1559480,

  title        = {Robust Uncertainty Quantification using Response Surface Approximations of Discontinuous Functions},

  author       = {Wildey, Timothy Michael and Gorodetsky, Alex and Belme, Anca and Shadid, John N.},

  abstractNote = {This paper considers response surface approximations for discontinuous quantities of interest. Our objective is not to adaptively characterize the manifold 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 manifolds. 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.},

  doi          = {10.1615/Int.J.UncertaintyQuantification.2019026974},

  journal      = {International Journal for Uncertainty Quantification},

  number       = 5,

  volume       = 9,

  place        = {United States},

  year         = {Tue Jan 01 00:00:00 EST 2019},

  month        = {Tue Jan 01 00:00:00 EST 2019}

}

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