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

doi:10.1007/s00158-019-02387-4

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 »« less

Authors:

Fernández-Godino, M. Giselle ^[1]; Dubreuil, Sylvain ^[2]; Bartoli, Nathalie ^[2]; Gogu, Christian ^[2]; Balachandar, S. ^[3];

^[3]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Université de Toulouse (France)
Univ. of Florida, Gainesville, FL (United States)

Publication Date:: 2019-10-14

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.

Copy to clipboard


                    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.

Copy to clipboard


                    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.

Copy to clipboard


                    
@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}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

DOI: 10.1007/s00158-019-02387-4

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 1 work

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

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

Sudret, Bruno
Reliability Engineering & System Safety, Vol. 93, Issue 7
DOI: 10.1016/j.ress.2007.04.002

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

Dubreuil, S.; Berveiller, M.; Petitjean, F.
Reliability Engineering & System Safety, Vol. 121
DOI: 10.1016/j.ress.2013.09.011

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

Le Gratiet, Loic; Garnier, Josselin
International Journal for Uncertainty Quantification, Vol. 4, Issue 5
DOI: 10.1615/Int.J.UncertaintyQuantification.2014006914

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

Blatman, Géraud; Sudret, Bruno
Journal of Computational Physics, Vol. 230, Issue 6
DOI: 10.1016/j.jcp.2010.12.021

Surrogate-based analysis and optimization
journal, January 2005

Queipo, Nestor V.; Haftka, Raphael T.; Shyy, Wei
Progress in Aerospace Sciences, Vol. 41, Issue 1
DOI: 10.1016/j.paerosci.2005.02.001

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

Blatman, Géraud; Sudret, Bruno
Reliability Engineering & System Safety, Vol. 95, Issue 11
DOI: 10.1016/j.ress.2010.06.015

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

Bouhlel, Mohamed Amine; Hwang, John T.; Bartoli, Nathalie
Advances in Engineering Software, Vol. 135
DOI: 10.1016/j.advengsoft.2019.03.005

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

Predicting the output from a complex computer code when fast approximations are available
journal, March 2000

Kennedy, M.
Biometrika, Vol. 87, Issue 1
DOI: 10.1093/biomet/87.1.1

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

Sobol′, I. M.
Mathematics and Computers in Simulation, Vol. 55, Issue 1-3
DOI: 10.1016/S0378-4754(00)00270-6

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

Similar Records in DOE PAGES and OSTI.GOV collections:

Multifidelity importance sampling

Journal Article Peherstorfer, Benjamin ; Cui, Tiangang ; Marzouk, Youssef ; ... - Computer Methods in Applied Mechanics and Engineering

Estimating statistics of model outputs with the Monte Carlo method usually requires a large number of model evaluations. This leads to long runtimes if the model is expensive to evaluate. Importance sampling is one method that can lead to a reduction in the number of model evaluations. Importance sampling uses a biasing distribution to sample the model more efficiently, but generating such a biasing distribution can be difficult and usually also requires model evaluations. A different strategy to speed up Monte Carlo sampling is to replace the computationally expensive high-fidelity model with a computationally cheap surrogate model; however, because themore »« less
Cited by 18
DOI: 10.1016/j.cma.2015.12.002

Full Text Available
Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization

Journal Article Peherstorfer, Benjamin ; Willcox, Karen ; Gunzburger, Max - SIAM Review

In many situations across computational science and engineering, multiple computational models are available that describe a system of interest. These different models have varying evaluation costs and varying fidelities. Typically, a computationally expensive high-fidelity model describes the system with the accuracy required by the current application at hand, while lower-fidelity models are less accurate but computationally cheaper than the high-fidelity model. Outer-loop applications, such as optimization, inference, and uncertainty quantification, require multiple model evaluations at many different inputs, which often leads to computational demands that exceed available resources if only the high-fidelity model is used. This work surveys multifidelity methodsmore »« less
Cited by 59
DOI: 10.1137/16m1082469

Full Text Available
When Bifidelity Meets CoKriging: An Efficient Physics-Informed Multifidelity Method

Journal Article Yang, Xiu ; Zhu, Xueyu ; Li, Jing - SIAM Journal on Scientific Computing

In this work, we propose a framework that combines the approximation-theory-based multifidelity method and Gaussian-process-regression-based multifidelity method to achieve data-model convergence when stochastic simulation models and sparse accurate observation data are available. Specifically, the two types of multifidelity methods we use are the bifidelity and CoKriging methods. The new approach uses the bifidelity method to efficiency estimate the empirical mean and covariance of the stochastic simulation outputs, then it uses these statistics to construct a Gaussian process (GP) representing low-fidelity in corking. We also combine the bifidelity method with Kriging, where the approximated empirical statistics are used to construct themore »« less
DOI: 10.1137/18M1231353
A Kriging Surrogate Model for Computing Gas Mixture Equations of State

Journal Article Ouellet, Frederick ; Park, Chanyoung ; Rollin, Bertrand ; ... - Journal of Fluids Engineering

Accurate simulation of the complex flow following the detonation of an explosive material is a challenging problem. In these flows, the detonation products of the explosive must be treated as a real gas while the surrounding air is treated as an ideal gas. As the detonation process unfolds and the blast wave moves into the surrounding ambient air, the products of detonation expand outward and interact with the air creating a mixture region. In this region, both of the state equations for air and the products must be satisfied. One of the most accurate, yet computationally expensive, methods to handlemore »« less
DOI: 10.1115/1.4042890
Multi-fidelity Gaussian process regression for prediction of random fields

Journal Article Parussini, L. ; Venturi, D., E-mail: venturi@ucsc.edu ; Perdikaris, P. ; ... - Journal of Computational Physics

We propose a new multi-fidelity Gaussian process regression (GPR) approach for prediction of random fields based on observations of surrogate models or hierarchies of surrogate models. Our method builds upon recent work on recursive Bayesian techniques, in particular recursive co-kriging, and extends it to vector-valued fields and various types of covariances, including separable and non-separable ones. The framework we propose is general and can be used to perform uncertainty propagation and quantification in model-based simulations, multi-fidelity data fusion, and surrogate-based optimization. We demonstrate the effectiveness of the proposed recursive GPR techniques through various examples. Specifically, we study the stochastic Burgersmore »« less
DOI: 10.1016/J.JCP.2017.01.047

Similar Records

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

Abstract

Citation Formats

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

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

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

Multifidelity Surrogate Based on Single Linear Regression journal, December 2018

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

Predicting the output from a complex computer code when fast approximations are available journal, March 2000

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

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

Matrix formulation of co-kriging journal, June 1982

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

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

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

Multifidelity Surrogate Based on Single Linear Regression
journal, December 2018

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

Predicting the output from a complex computer code when fast approximations are available
journal, March 2000

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

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

Matrix formulation of co-kriging
journal, June 1982