skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Linear Regression Based Multi-fidelity Surrogate for Disturbance Amplification in Multi-phase Explosion

Abstract

When simulations are very expensive and many are required, as for optimization or uncertainty quantification, a way to reduce cost is using surrogates. With multiple simulations to predict the quantity of interest, some being very expensive and accurate (high-fidelity simulations) and others cheaper but less accurate (low-fidelity simulations), it may be worthwhile to use multifidelity surrogates (MFSs). Moreover, if we can afford just a few high-fidelity simulations or experiments, MFS becomes necessary. Co-Kriging, which is probably the most popular MFS, replaces both low-fidelity and high-fidelity simulations by a single MFS. A recently proposed linear regression–based MFS (LR-MFS) offers the option to correct the LF simulations instead of correcting the LF surrogate in the MFS. When the low-fidelity simulation is cheap enough for use in an application, such as optimization, this may be an attractive option. Here, we explore the performance of LR-MFS using exact and surrogate-replaced low-fidelity simulations. The concern studied is a cylindrical dispersal of 100-μ m-diameter solid particles after detonation and the quantity of interest is a measure of the amplification of the departure from axisymmetry. We find very substantial accuracy improvements for this problem using the LR-MFS with exact low-fidelity simulations. Inspired by these results, we alsomore » compare the performance of co-Kriging to the use of Kriging to correct exact low-fidelity simulations and find a similar accuracy improvement when simulations are directly used. For this problem, further improvements in accuracy are achievable by taking advantage of inherent parametric symmetries. These findings may alert users of MFSs to the possible advantages of using exact low-fidelity simulations when this is affordable.« less

Authors:
 [1];  [2];  [2];  [2];  [3]; ORCiD logo [3]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Université de Toulouse (France)
  3. Univ. of Florida, Gainesville, FL (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1571620
Report Number(s):
LA-UR-19-22491
Journal ID: ISSN 1615-147X
Grant/Contract Number:  
89233218CNA000001; NA0002378
Resource Type:
Accepted Manuscript
Journal Name:
Structural and Multidisciplinary Optimization
Additional Journal Information:
Journal Volume: 60; Journal Issue: 6; Journal ID: ISSN 1615-147X
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; Multifidelity; Surrogates; Symmetries; Linear regression; Kriging; Co-Kriging

Citation Formats

Fernández-Godino, M. Giselle, Dubreuil, Sylvain, Bartoli, Nathalie, Gogu, Christian, Balachandar, S., and Haftka, Raphael T. Linear Regression Based Multi-fidelity Surrogate for Disturbance Amplification in Multi-phase Explosion. United States: N. p., 2019. Web. doi:10.1007/s00158-019-02387-4.
Fernández-Godino, M. Giselle, Dubreuil, Sylvain, Bartoli, Nathalie, Gogu, Christian, Balachandar, S., & Haftka, Raphael T. Linear Regression Based Multi-fidelity Surrogate for Disturbance Amplification in Multi-phase Explosion. United States. doi:10.1007/s00158-019-02387-4.
Fernández-Godino, M. Giselle, Dubreuil, Sylvain, Bartoli, Nathalie, Gogu, Christian, Balachandar, S., and Haftka, Raphael T. Mon . "Linear Regression Based Multi-fidelity Surrogate for Disturbance Amplification in Multi-phase Explosion". United States. doi:10.1007/s00158-019-02387-4. https://www.osti.gov/servlets/purl/1571620.
@article{osti_1571620,
title = {Linear Regression Based Multi-fidelity Surrogate for Disturbance Amplification in Multi-phase Explosion},
author = {Fernández-Godino, M. Giselle and Dubreuil, Sylvain and Bartoli, Nathalie and Gogu, Christian and Balachandar, S. and Haftka, Raphael T.},
abstractNote = {When simulations are very expensive and many are required, as for optimization or uncertainty quantification, a way to reduce cost is using surrogates. With multiple simulations to predict the quantity of interest, some being very expensive and accurate (high-fidelity simulations) and others cheaper but less accurate (low-fidelity simulations), it may be worthwhile to use multifidelity surrogates (MFSs). Moreover, if we can afford just a few high-fidelity simulations or experiments, MFS becomes necessary. Co-Kriging, which is probably the most popular MFS, replaces both low-fidelity and high-fidelity simulations by a single MFS. A recently proposed linear regression–based MFS (LR-MFS) offers the option to correct the LF simulations instead of correcting the LF surrogate in the MFS. When the low-fidelity simulation is cheap enough for use in an application, such as optimization, this may be an attractive option. Here, we explore the performance of LR-MFS using exact and surrogate-replaced low-fidelity simulations. The concern studied is a cylindrical dispersal of 100-μ m-diameter solid particles after detonation and the quantity of interest is a measure of the amplification of the departure from axisymmetry. We find very substantial accuracy improvements for this problem using the LR-MFS with exact low-fidelity simulations. Inspired by these results, we also compare the performance of co-Kriging to the use of Kriging to correct exact low-fidelity simulations and find a similar accuracy improvement when simulations are directly used. For this problem, further improvements in accuracy are achievable by taking advantage of inherent parametric symmetries. These findings may alert users of MFSs to the possible advantages of using exact low-fidelity simulations when this is affordable.},
doi = {10.1007/s00158-019-02387-4},
journal = {Structural and Multidisciplinary Optimization},
number = 6,
volume = 60,
place = {United States},
year = {2019},
month = {10}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 1 work
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Effect of a bimodal initial particle volume fraction perturbation in an explosive dispersal of particles
conference, January 2017

  • Ouellet, Frederick; Annamalai, Subramanian; Rollin, Bertrand
  • SHOCK COMPRESSION OF CONDENSED MATTER - 2015: Proceedings of the Conference of the American Physical Society Topical Group on Shock Compression of Condensed Matter, AIP Conference Proceedings
  • DOI: 10.1063/1.4971740

Global sensitivity analysis using polynomial chaos expansions
journal, July 2008


Construction of bootstrap confidence intervals on sensitivity indices computed by polynomial chaos expansion
journal, January 2014


Recursive Co-Kriging Model for Design of Computer Experiments with Multiple Levels of Fidelity
journal, January 2014


On the Use of Symmetries in Building Surrogate Models
journal, January 2019

  • Giselle Fernández-Godino, M.; Balachandar, S.; Haftka, Raphael T.
  • Journal of Mechanical Design, Vol. 141, Issue 6
  • DOI: 10.1115/1.4042047

Adaptive sparse polynomial chaos expansion based on least angle regression
journal, March 2011


Surrogate-based analysis and optimization
journal, January 2005


Efficient computation of global sensitivity indices using sparse polynomial chaos expansions
journal, November 2010


Issues in Deciding Whether to Use Multifidelity Surrogates
journal, May 2019

  • Giselle Fernández-Godino, M.; Park, Chanyoung; Kim, Nam H.
  • AIAA Journal, Vol. 57, Issue 5
  • DOI: 10.2514/1.J057750

Multifidelity Surrogate Based on Single Linear Regression
journal, December 2018

  • Zhang, Yiming; Kim, Nam H.; Park, Chanyoung
  • AIAA Journal, Vol. 56, Issue 12
  • DOI: 10.2514/1.J057299

A Python surrogate modeling framework with derivatives
journal, September 2019


Early Time Evolution of Circumferential Perturbation of Initial Particle Volume Fraction in Explosive Cylindrical Multiphase Dispersion
journal, April 2019

  • Fernández-Godino, M. Giselle; Ouellet, Frederick; Haftka, Raphael T.
  • Journal of Fluids Engineering, Vol. 141, Issue 9
  • DOI: 10.1115/1.4043055

The Orthogonal Development of Non-Linear Functionals in Series of Fourier-Hermite Functionals
journal, April 1947

  • Cameron, R. H.; Martin, W. T.
  • The Annals of Mathematics, Vol. 48, Issue 2
  • DOI: 10.2307/1969178

Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates
journal, February 2001


Effects of Initial Perturbations in the Early Moments of an Explosive Dispersal of Particles
journal, April 2016

  • Annamalai, Subramanian; Rollin, Bertrand; Ouellet, Frederick
  • Journal of Fluids Engineering, Vol. 138, Issue 7
  • DOI: 10.1115/1.4030954

Matrix formulation of co-kriging
journal, June 1982

  • Myers, Donald E.
  • Journal of the International Association for Mathematical Geology, Vol. 14, Issue 3
  • DOI: 10.1007/BF01032887