@article{2a3f85c1c734405ea8e25d235e470b01,
title = "Sliced-inverse-regression-aided rotated compressive sensing method for uncertainty quantification",
abstract = "Compressive-sensing-based uncertainty quantifie ation methods have become a powerful tool for problems with limited data. In this work, we use the sliced inverse regression (SIR) method to provide an initial guess for the alternating direction method, which is used to enhance sparsity of the Hermite polynomial expansion of a stochastic quantity of interest. The sparsity improvement increases both the efficiency and accuracy of the compressive-sensing-based uncertainty quantification method. We demonstrate that the initial guess from SIR is suitable for cases when the available data are limited (Algorithm 3.2). We also propose another algorithm (Algorithm 3.3) that performs dimension reduction first with SIR. Then it constructs a Hermite polynomial expansion of the reduced model. This method affords the ability to approximate t he statistics accurately with even less available data. Both methods are nonintrusive and require no a priori information of the sparsity of the system. The effectiveness of these two methods (Algorithms 3.2 and 3.3) is demonstrated using problems with up to 500 random dimensions.",
keywords = "Alternating direction method, Compressive sensing, Iterative rotation, Sliced inverse regression, Uncertainty quantification",
author = "Xiu Yang and Weixuan Li and Alexandre Tartakovsky",
note = "Funding Information: This work was supported by the U.S. Department of Energy (DOE), Office of Science, Office of Advanced Scientific Computing Research (ASCR) as part of the Multifaceted Mathematics for Complex Systems project and the Uncertainty Quantification in Advection-Diffusion-Reaction Systems projects. A portion of the research described in this paper was conducted under the Laboratory Directed Research and Development Program at Pacific Northwest National Laboratory (PNNL). PNNL is operated by Battelle for the DOE under contract DE-AC05-76RL01830. The U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for U.S. Government purposes. Copyright is owned by SIAM to the extent not limited by these rights. Funding Information: \ast Received by the editors September 25, 2017; accepted for publication (in revised form) September 13, 2018; published electronically November 6, 2018. http://www.siam.org/journals/juq/6-4/M114895.html Funding: This work was supported by the U.S. Department of Energy (DOE), Office of Science, Office of Advanced Scientific Computing Research (ASCR) as part of the Multifaceted Mathematics for Complex Systems project and the Uncertainty Quantification in Advection-Diffusion-Reaction Systems projects. A portion of the research described in this paper was conducted under the Laboratory Directed Research and Development Program at Pacific Northwest National Laboratory (PNNL). PNNL is operated by Battelle for the DOE under contract DE-AC05-76RL01830. The U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for U.S. Government purposes. Copyright is owned by SIAM to the extent not limited by these rights. Publisher Copyright: {\textcopyright} 2018 Society for Industrial and Applied Mathematics and American Statistical Association",
year = "2018",
doi = "10.1137/17M1148955",
language = "English (US)",
volume = "6",
pages = "1532--1554",
journal = "SIAM-ASA Journal on Uncertainty Quantification",
issn = "2166-2525",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "4",
}