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Title: Gradient-Free Construction of Active Subspaces for Dimension Reduction in Complex Models with Applications to Neutronics

Abstract

Recent developments in the field of reduced-order modeling---and, in particular, active subspace construction---have made it possible to efficiently approximate complex models by constructing low-order response surfaces based upon a small subspace of the original high-dimensional parameter space. These methods rely upon the fact that the response tends to vary more prominently in a few dominant directions defined by linear combinations of the original inputs, allowing for a rotation of the coordinate axis and a consequent transformation of the parameters. In this work, we discuss a gradient-free active subspace algorithm that is feasible for high-dimensional parameter spaces where finite-difference techniques are impractical. This analysis extends the gradient-free algorithm introduced in [A. Lewis, R. Smith, and B. Williams, Comput. Math. Appl., 72 (2016), pp. 1603--1615] in two significant ways: (i) we introduce an initialization algorithm to identify lower-dimensional subspaces of influential directions to seed the gradient-free algorithm for high-dimensional problems, and (ii) we analyze dimension selection criteria to verify the algorithms. Finally, we illustrate the initialized gradient-free active subspace algorithm for a neutronics example implemented with SCALE6.1 for input dimensions up to 7700.

Authors:
 [1];  [2];  [1]; ORCiD logo [3];  [4];  [5]
  1. North Carolina State Univ., Raleigh, NC (United States)
  2. Lafayette College, Easton, PA (United States)
  3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  4. Iowa State Univ., Ames, IA (United States)
  5. University of Sharjah (United Arab Emirates)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Office of Nuclear Energy (NE)
OSTI Identifier:
1530778
Report Number(s):
LA-UR-18-25392
Journal ID: ISSN 2166-2525
Grant/Contract Number:  
89233218CNA000001; AC05-00OR22725
Resource Type:
Accepted Manuscript
Journal Name:
SIAM/ASA Journal on Uncertainty Quantification
Additional Journal Information:
Journal Volume: 7; Journal Issue: 1; Journal ID: ISSN 2166-2525
Publisher:
SIAM
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; gradient-free active subspaces; neutronics applications

Citation Formats

Coleman, Kayla D., Lewis, Allison, Smith, Ralph C., Williams, Brian J., Morris, Max D., and Khuwaileh, Bassam. Gradient-Free Construction of Active Subspaces for Dimension Reduction in Complex Models with Applications to Neutronics. United States: N. p., 2019. Web. doi:10.1137/16M1075119.
Coleman, Kayla D., Lewis, Allison, Smith, Ralph C., Williams, Brian J., Morris, Max D., & Khuwaileh, Bassam. Gradient-Free Construction of Active Subspaces for Dimension Reduction in Complex Models with Applications to Neutronics. United States. doi:10.1137/16M1075119.
Coleman, Kayla D., Lewis, Allison, Smith, Ralph C., Williams, Brian J., Morris, Max D., and Khuwaileh, Bassam. Thu . "Gradient-Free Construction of Active Subspaces for Dimension Reduction in Complex Models with Applications to Neutronics". United States. doi:10.1137/16M1075119.
@article{osti_1530778,
title = {Gradient-Free Construction of Active Subspaces for Dimension Reduction in Complex Models with Applications to Neutronics},
author = {Coleman, Kayla D. and Lewis, Allison and Smith, Ralph C. and Williams, Brian J. and Morris, Max D. and Khuwaileh, Bassam},
abstractNote = {Recent developments in the field of reduced-order modeling---and, in particular, active subspace construction---have made it possible to efficiently approximate complex models by constructing low-order response surfaces based upon a small subspace of the original high-dimensional parameter space. These methods rely upon the fact that the response tends to vary more prominently in a few dominant directions defined by linear combinations of the original inputs, allowing for a rotation of the coordinate axis and a consequent transformation of the parameters. In this work, we discuss a gradient-free active subspace algorithm that is feasible for high-dimensional parameter spaces where finite-difference techniques are impractical. This analysis extends the gradient-free algorithm introduced in [A. Lewis, R. Smith, and B. Williams, Comput. Math. Appl., 72 (2016), pp. 1603--1615] in two significant ways: (i) we introduce an initialization algorithm to identify lower-dimensional subspaces of influential directions to seed the gradient-free algorithm for high-dimensional problems, and (ii) we analyze dimension selection criteria to verify the algorithms. Finally, we illustrate the initialized gradient-free active subspace algorithm for a neutronics example implemented with SCALE6.1 for input dimensions up to 7700.},
doi = {10.1137/16M1075119},
journal = {SIAM/ASA Journal on Uncertainty Quantification},
number = 1,
volume = 7,
place = {United States},
year = {2019},
month = {1}
}

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