GradientFree Construction of Active Subspaces for Dimension Reduction in Complex Models with Applications to Neutronics
Abstract
Recent developments in the field of reducedorder modelingand, in particular, active subspace constructionhave made it possible to efficiently approximate complex models by constructing loworder response surfaces based upon a small subspace of the original highdimensional 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 gradientfree active subspace algorithm that is feasible for highdimensional parameter spaces where finitedifference techniques are impractical. This analysis extends the gradientfree algorithm introduced in [A. Lewis, R. Smith, and B. Williams, Comput. Math. Appl., 72 (2016), pp. 16031615] in two significant ways: (i) we introduce an initialization algorithm to identify lowerdimensional subspaces of influential directions to seed the gradientfree algorithm for highdimensional problems, and (ii) we analyze dimension selection criteria to verify the algorithms. Finally, we illustrate the initialized gradientfree active subspace algorithm for a neutronics example implemented with SCALE6.1 for input dimensions up to 7700.
 Authors:

 North Carolina State Univ., Raleigh, NC (United States)
 Lafayette College, Easton, PA (United States)
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Iowa State Univ., Ames, IA (United States)
 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):
 LAUR1825392
Journal ID: ISSN 21662525
 Grant/Contract Number:
 89233218CNA000001; AC0500OR22725
 Resource Type:
 Accepted Manuscript
 Journal Name:
 SIAM/ASA Journal on Uncertainty Quantification
 Additional Journal Information:
 Journal Volume: 7; Journal Issue: 1; Journal ID: ISSN 21662525
 Publisher:
 SIAM
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; gradientfree active subspaces; neutronics applications
Citation Formats
Coleman, Kayla D., Lewis, Allison, Smith, Ralph C., Williams, Brian J., Morris, Max D., and Khuwaileh, Bassam. GradientFree 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. GradientFree 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 .
"GradientFree Construction of Active Subspaces for Dimension Reduction in Complex Models with Applications to Neutronics". United States. doi:10.1137/16M1075119. https://www.osti.gov/servlets/purl/1530778.
@article{osti_1530778,
title = {GradientFree 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 reducedorder modelingand, in particular, active subspace constructionhave made it possible to efficiently approximate complex models by constructing loworder response surfaces based upon a small subspace of the original highdimensional 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 gradientfree active subspace algorithm that is feasible for highdimensional parameter spaces where finitedifference techniques are impractical. This analysis extends the gradientfree algorithm introduced in [A. Lewis, R. Smith, and B. Williams, Comput. Math. Appl., 72 (2016), pp. 16031615] in two significant ways: (i) we introduce an initialization algorithm to identify lowerdimensional subspaces of influential directions to seed the gradientfree algorithm for highdimensional problems, and (ii) we analyze dimension selection criteria to verify the algorithms. Finally, we illustrate the initialized gradientfree 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}
}