Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates

Jakeman, J. D.; Wildey, T.

doi:10.1016/j.jcp.2014.09.014

Title: Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates

Journal Article · Thu Jan 01 00:00:00 EST 2015 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2014.09.014· OSTI ID:1123534

^[1]; Wildey, T. ^[1]

Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the interpolation error in the sparse grid to enhance the sparse grid approximation and to drive adaptivity. We show that utilizing these error estimates provides significantly more accurate functional values for random samples of the sparse grid approximation. We also demonstrate that alternative refinement strategies based upon a posteriori error estimates can lead to further increases in accuracy in the approximation over traditional hierarchical surplus based strategies. Throughout this paper we also provide and test a framework for balancing the physical discretization error with the stochastic interpolation error of the enhanced sparse grid approximation.

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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:: 1123534

Alternate ID(s):: OSTI ID: 1247015

Report Number(s):: SAND-2013-10657J; PII: S0021999114006500

Journal Information:: Journal of Computational Physics, Vol. 280, Issue C; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 13 works

Citation information provided by
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Enhanced adaptive surrogate models with applications in uncertainty quantification for nanoplasmonics Georg, Niklas; Loukrezis, Dimitrios; Römer, Ulrich arXiv https://doi.org/10.48550/arxiv.1807.07485	text	January 2018
Robust Uncertainty Quantification Using Response Surface Approximations of Discontinuous Functions Wildey, Timothy; Gorodetsky, A. A.; Belme, A. International Journal for Uncertainty Quantification, Vol. 9, Issue 5 https://doi.org/10.1615/int.j.uncertaintyquantification.2019026974	journal	January 2019
Convergence of Probability Densities using Approximate Models for Forward and Inverse Problems in Uncertainty Quantification Butler, T.; Jakeman, J. D.; Wildey, T. arXiv https://doi.org/10.48550/arxiv.1807.00375	text	January 2018
Assessing the Performance of leja and Clenshaw-Curtis Collocation for Computational Electromagnetics with Random Input data Loukrezis, Dimitrios; Römer, Ulrich; De Gersem, Herbert International Journal for Uncertainty Quantification, Vol. 9, Issue 1 https://doi.org/10.1615/int.j.uncertaintyquantification.2018025234	journal	January 2019
A generalized sampling and preconditioning scheme for sparse approximation of polynomial chaos expansions Jakeman, John D.; Narayan, Akil; Zhou, Tao arXiv https://doi.org/10.48550/arxiv.1602.06879	text	January 2016
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