Monte Carlo estimation of sparse grid interpolation residual for stochastic collocation of high-order systems with uncertainties

Xu Chen; Xiao Ma; Aosheng Rong; Jose E. Schutt-Aine; Andreas C. Cangellaris

doi:10.1109/SaPIW.2017.7944004

Monte Carlo estimation of sparse grid interpolation residual for stochastic collocation of high-order systems with uncertainties

Xu Chen, Xiao Ma, Aosheng Rong, Jose E. Schutt-Aine, Andreas C. Cangellaris

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

In fast sampling-based stochastic numerical techniques, Smolyak-based sparse grids are used to construct interpolation of the system output in random domain. The accuracy and convergence of sparse grid interpolations are evaluated by calculating the residual of the interpolation outputs compared with actual output values at grid nodes of higher levels. The residual is used as a criteria for adaptive refinement, as well as local refinement of sparse grids. In this paper, we propose a Monte Carlo sampling-based method to estimate the residual of sparse grid interpolations.

Original language	English (US)
Title of host publication	2017 IEEE 21st Workshop on Signal and Power Integrity, SPI 2017 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)	9781509056163
DOIs	https://doi.org/10.1109/SaPIW.2017.7944004
State	Published - Jun 7 2017
Event	21st IEEE Workshop on Signal and Power Integrity, SPI 2017 - Lake Maggiore (Baveno), Italy Duration: May 7 2017 → May 10 2017

Publication series

Name	2017 IEEE 21st Workshop on Signal and Power Integrity, SPI 2017 - Proceedings

Other

Other	21st IEEE Workshop on Signal and Power Integrity, SPI 2017
Country/Territory	Italy
City	Lake Maggiore (Baveno)
Period	5/7/17 → 5/10/17

ASJC Scopus subject areas

Computer Networks and Communications
Hardware and Architecture
Signal Processing

Online availability

10.1109/SaPIW.2017.7944004

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Chen, X., Ma, X., Rong, A., Schutt-Aine, J. E., & Cangellaris, A. C. (2017). Monte Carlo estimation of sparse grid interpolation residual for stochastic collocation of high-order systems with uncertainties. In 2017 IEEE 21st Workshop on Signal and Power Integrity, SPI 2017 - Proceedings Article 7944004 (2017 IEEE 21st Workshop on Signal and Power Integrity, SPI 2017 - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/SaPIW.2017.7944004

Monte Carlo estimation of sparse grid interpolation residual for stochastic collocation of high-order systems with uncertainties. / Chen, Xu; Ma, Xiao; Rong, Aosheng et al.
2017 IEEE 21st Workshop on Signal and Power Integrity, SPI 2017 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2017. 7944004 (2017 IEEE 21st Workshop on Signal and Power Integrity, SPI 2017 - Proceedings).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Chen, X, Ma, X, Rong, A, Schutt-Aine, JE & Cangellaris, AC 2017, Monte Carlo estimation of sparse grid interpolation residual for stochastic collocation of high-order systems with uncertainties. in 2017 IEEE 21st Workshop on Signal and Power Integrity, SPI 2017 - Proceedings., 7944004, 2017 IEEE 21st Workshop on Signal and Power Integrity, SPI 2017 - Proceedings, Institute of Electrical and Electronics Engineers Inc., 21st IEEE Workshop on Signal and Power Integrity, SPI 2017, Lake Maggiore (Baveno), Italy, 5/7/17. https://doi.org/10.1109/SaPIW.2017.7944004

Chen X, Ma X, Rong A, Schutt-Aine JE , Cangellaris AC. Monte Carlo estimation of sparse grid interpolation residual for stochastic collocation of high-order systems with uncertainties. In 2017 IEEE 21st Workshop on Signal and Power Integrity, SPI 2017 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2017. 7944004. (2017 IEEE 21st Workshop on Signal and Power Integrity, SPI 2017 - Proceedings). doi: 10.1109/SaPIW.2017.7944004

Chen, Xu ; Ma, Xiao ; Rong, Aosheng et al. / Monte Carlo estimation of sparse grid interpolation residual for stochastic collocation of high-order systems with uncertainties. 2017 IEEE 21st Workshop on Signal and Power Integrity, SPI 2017 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2017. (2017 IEEE 21st Workshop on Signal and Power Integrity, SPI 2017 - Proceedings).

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AB - In fast sampling-based stochastic numerical techniques, Smolyak-based sparse grids are used to construct interpolation of the system output in random domain. The accuracy and convergence of sparse grid interpolations are evaluated by calculating the residual of the interpolation outputs compared with actual output values at grid nodes of higher levels. The residual is used as a criteria for adaptive refinement, as well as local refinement of sparse grids. In this paper, we propose a Monte Carlo sampling-based method to estimate the residual of sparse grid interpolations.

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Monte Carlo estimation of sparse grid interpolation residual for stochastic collocation of high-order systems with uncertainties

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