Robust Uncertainty Quantification using Response Surface Approximations of Discontinuous Functions
- 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)
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.
- Research Organization:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- Grant/Contract Number:
- AC04-94AL85000
- OSTI ID:
- 1559480
- Report Number(s):
- SAND-2019-4016J; 674563
- Journal Information:
- International Journal for Uncertainty Quantification, Vol. 9, Issue 5; ISSN 2152-5080
- Publisher:
- Begell HouseCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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