A priori testing of sparse adaptive polynomial chaos expansions using an ocean general circulation model database

Justin Winokur; Patrick Conrad; Ihab Sraj; Omar Knio; Ashwanth Srinivasan; W. Carlisle Thacker; Youssef Marzouk; Mohamed Iskandarani

doi:10.1007/s10596-013-9361-3

A priori testing of sparse adaptive polynomial chaos expansions using an ocean general circulation model database

Justin Winokur, Patrick Conrad, Ihab Sraj, Omar Knio, Ashwanth Srinivasan, W. Carlisle Thacker, Youssef Marzouk, Mohamed Iskandarani^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

36 Scopus citations

Abstract

This work explores the implementation of an adaptive strategy to design sparse ensembles of oceanic simulations suitable for constructing polynomial chaos surrogates. We use a recently developed pseudo-spectral algorithm that is based on a direct application of the Smolyak sparse grid formula and that allows the use of arbitrary admissible sparse grids. The adaptive algorithm is tested using an existing simulation database of the oceanic response to Hurricane Ivan in the Gulf of Mexico. The a priori tests demonstrate that sparse and adaptive pseudo-spectral constructions lead to substantial savings over isotropic sparse sampling in the present setting.

Original language	English (US)
Pages (from-to)	899-911
Number of pages	13
Journal	Computational Geosciences
Volume	17
Issue number	6
DOIs	https://doi.org/10.1007/s10596-013-9361-3
State	Published - Dec 2013

Bibliographical note

Funding Information:
Acknowledgments This research was supported by the Office of Naval Research, award N00014-101-0498; by the US Department of Energy, Office of Advanced Scientific Computing Research, award numbers DE-SC0007020, DE-SC0008789, and DE-SC0007099; and by the Gulf of Mexico Research Initiative, contract numbers SA1207GOMRI005 (CARTHE) and SA12GOMRI008 (DEEP-C).

Keywords

Adaptive sampling
Ocean modeling
Polynomial chaos
Sparse Smolyak quadrature
Uncertainty quantification

ASJC Scopus subject areas

Computers in Earth Sciences
Computational Mathematics
Computer Science Applications
Computational Theory and Mathematics

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10.1007/s10596-013-9361-3

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title = "A priori testing of sparse adaptive polynomial chaos expansions using an ocean general circulation model database",

abstract = "This work explores the implementation of an adaptive strategy to design sparse ensembles of oceanic simulations suitable for constructing polynomial chaos surrogates. We use a recently developed pseudo-spectral algorithm that is based on a direct application of the Smolyak sparse grid formula and that allows the use of arbitrary admissible sparse grids. The adaptive algorithm is tested using an existing simulation database of the oceanic response to Hurricane Ivan in the Gulf of Mexico. The a priori tests demonstrate that sparse and adaptive pseudo-spectral constructions lead to substantial savings over isotropic sparse sampling in the present setting.",

keywords = "Adaptive sampling, Ocean modeling, Polynomial chaos, Sparse Smolyak quadrature, Uncertainty quantification",

author = "Justin Winokur and Patrick Conrad and Ihab Sraj and Omar Knio and Ashwanth Srinivasan and Thacker, {W. Carlisle} and Youssef Marzouk and Mohamed Iskandarani",

note = "Funding Information: Acknowledgments This research was supported by the Office of Naval Research, award N00014-101-0498; by the US Department of Energy, Office of Advanced Scientific Computing Research, award numbers DE-SC0007020, DE-SC0008789, and DE-SC0007099; and by the Gulf of Mexico Research Initiative, contract numbers SA1207GOMRI005 (CARTHE) and SA12GOMRI008 (DEEP-C).",

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doi = "10.1007/s10596-013-9361-3",

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AU - Conrad, Patrick

AU - Sraj, Ihab

AU - Knio, Omar

AU - Srinivasan, Ashwanth

AU - Thacker, W. Carlisle

AU - Marzouk, Youssef

AU - Iskandarani, Mohamed

N1 - Funding Information: Acknowledgments This research was supported by the Office of Naval Research, award N00014-101-0498; by the US Department of Energy, Office of Advanced Scientific Computing Research, award numbers DE-SC0007020, DE-SC0008789, and DE-SC0007099; and by the Gulf of Mexico Research Initiative, contract numbers SA1207GOMRI005 (CARTHE) and SA12GOMRI008 (DEEP-C).

PY - 2013/12

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N2 - This work explores the implementation of an adaptive strategy to design sparse ensembles of oceanic simulations suitable for constructing polynomial chaos surrogates. We use a recently developed pseudo-spectral algorithm that is based on a direct application of the Smolyak sparse grid formula and that allows the use of arbitrary admissible sparse grids. The adaptive algorithm is tested using an existing simulation database of the oceanic response to Hurricane Ivan in the Gulf of Mexico. The a priori tests demonstrate that sparse and adaptive pseudo-spectral constructions lead to substantial savings over isotropic sparse sampling in the present setting.

AB - This work explores the implementation of an adaptive strategy to design sparse ensembles of oceanic simulations suitable for constructing polynomial chaos surrogates. We use a recently developed pseudo-spectral algorithm that is based on a direct application of the Smolyak sparse grid formula and that allows the use of arbitrary admissible sparse grids. The adaptive algorithm is tested using an existing simulation database of the oceanic response to Hurricane Ivan in the Gulf of Mexico. The a priori tests demonstrate that sparse and adaptive pseudo-spectral constructions lead to substantial savings over isotropic sparse sampling in the present setting.

KW - Adaptive sampling

KW - Ocean modeling

KW - Polynomial chaos

KW - Sparse Smolyak quadrature

KW - Uncertainty quantification

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ER -

A priori testing of sparse adaptive polynomial chaos expansions using an ocean general circulation model database

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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