On the use of kriging models to approximate deterministic computer models

Research output: Contribution to conferencePaper

43 Citations (Scopus)

Abstract

The use of kriging models for approximation and metamodel-based design and optimization has been steadily on the rise in the past decade. The widespread usage of kriging models appears to be hampered by (1) the lack of guidance in selecting the appropriate form of the kriging model, (2) computationally efficient algorithms for estimating the model's parameters, and (3) an effective method to assess the resulting model's quality. In this paper, we compare (1) Maximum Likelihood Estimation (MLE) and Cross-Validation (CV) parameter estimation methods for selecting a kriging model's parameters given its form and (2) and an R2 of prediction and the corrected Akaike Information Criterion for assessing the quality of the created kriging model, permitting the comparison of different forms of a kriging model. These methods are demonstrated with six test problems. Finally, different forms of kriging models are examined to determine if more complex forms are more accurate and easier to fit than simple forms of kriging models for approximating computer models.

Original languageEnglish (US)
Pages481-492
Number of pages12
StatePublished - Dec 1 2004
Event2004 ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference - Salt Lake City, UT, United States
Duration: Sep 28 2004Oct 2 2004

Other

Other2004 ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference
CountryUnited States
CitySalt Lake City, UT
Period9/28/0410/2/04

Fingerprint

Kriging
Computer Model
Deterministic Model
Model
Akaike Information Criterion
Maximum likelihood estimation
Metamodel
Maximum Likelihood Estimation
Cross-validation
Test Problems
Guidance
Parameter Estimation
Form
Parameter estimation
Efficient Algorithms
Optimization
Prediction

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Mechanical Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design

Cite this

Martin, J. D., & Simpson, T. W. (2004). On the use of kriging models to approximate deterministic computer models. 481-492. Paper presented at 2004 ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Salt Lake City, UT, United States.
Martin, Jay Dean ; Simpson, Timothy William. / On the use of kriging models to approximate deterministic computer models. Paper presented at 2004 ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Salt Lake City, UT, United States.12 p.
@conference{b47b7d49cafb4c8fac0cae7d53b059f3,
title = "On the use of kriging models to approximate deterministic computer models",
abstract = "The use of kriging models for approximation and metamodel-based design and optimization has been steadily on the rise in the past decade. The widespread usage of kriging models appears to be hampered by (1) the lack of guidance in selecting the appropriate form of the kriging model, (2) computationally efficient algorithms for estimating the model's parameters, and (3) an effective method to assess the resulting model's quality. In this paper, we compare (1) Maximum Likelihood Estimation (MLE) and Cross-Validation (CV) parameter estimation methods for selecting a kriging model's parameters given its form and (2) and an R2 of prediction and the corrected Akaike Information Criterion for assessing the quality of the created kriging model, permitting the comparison of different forms of a kriging model. These methods are demonstrated with six test problems. Finally, different forms of kriging models are examined to determine if more complex forms are more accurate and easier to fit than simple forms of kriging models for approximating computer models.",
author = "Martin, {Jay Dean} and Simpson, {Timothy William}",
year = "2004",
month = "12",
day = "1",
language = "English (US)",
pages = "481--492",
note = "2004 ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference ; Conference date: 28-09-2004 Through 02-10-2004",

}

Martin, JD & Simpson, TW 2004, 'On the use of kriging models to approximate deterministic computer models' Paper presented at 2004 ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Salt Lake City, UT, United States, 9/28/04 - 10/2/04, pp. 481-492.

On the use of kriging models to approximate deterministic computer models. / Martin, Jay Dean; Simpson, Timothy William.

2004. 481-492 Paper presented at 2004 ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Salt Lake City, UT, United States.

Research output: Contribution to conferencePaper

TY - CONF

T1 - On the use of kriging models to approximate deterministic computer models

AU - Martin, Jay Dean

AU - Simpson, Timothy William

PY - 2004/12/1

Y1 - 2004/12/1

N2 - The use of kriging models for approximation and metamodel-based design and optimization has been steadily on the rise in the past decade. The widespread usage of kriging models appears to be hampered by (1) the lack of guidance in selecting the appropriate form of the kriging model, (2) computationally efficient algorithms for estimating the model's parameters, and (3) an effective method to assess the resulting model's quality. In this paper, we compare (1) Maximum Likelihood Estimation (MLE) and Cross-Validation (CV) parameter estimation methods for selecting a kriging model's parameters given its form and (2) and an R2 of prediction and the corrected Akaike Information Criterion for assessing the quality of the created kriging model, permitting the comparison of different forms of a kriging model. These methods are demonstrated with six test problems. Finally, different forms of kriging models are examined to determine if more complex forms are more accurate and easier to fit than simple forms of kriging models for approximating computer models.

AB - The use of kriging models for approximation and metamodel-based design and optimization has been steadily on the rise in the past decade. The widespread usage of kriging models appears to be hampered by (1) the lack of guidance in selecting the appropriate form of the kriging model, (2) computationally efficient algorithms for estimating the model's parameters, and (3) an effective method to assess the resulting model's quality. In this paper, we compare (1) Maximum Likelihood Estimation (MLE) and Cross-Validation (CV) parameter estimation methods for selecting a kriging model's parameters given its form and (2) and an R2 of prediction and the corrected Akaike Information Criterion for assessing the quality of the created kriging model, permitting the comparison of different forms of a kriging model. These methods are demonstrated with six test problems. Finally, different forms of kriging models are examined to determine if more complex forms are more accurate and easier to fit than simple forms of kriging models for approximating computer models.

UR - http://www.scopus.com/inward/record.url?scp=14044253615&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=14044253615&partnerID=8YFLogxK

M3 - Paper

AN - SCOPUS:14044253615

SP - 481

EP - 492

ER -

Martin JD, Simpson TW. On the use of kriging models to approximate deterministic computer models. 2004. Paper presented at 2004 ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Salt Lake City, UT, United States.