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

Title: A Theoretical Framework for Calibration in Computer Models: Parametrization, Estimation and Convergence Properties

Abstract

Calibration parameters in deterministic computer experiments are those attributes that cannot be measured or available in physical experiments. Here, an approach to estimate them by using data from physical experiments and computer simulations. A theoretical framework is given which allows us to study the issues of parameter identifiability and estimation. We define the L 2-consistency for calibration as a justification for calibration methods. It is shown that a simplified version of the original KO method leads to asymptotically L 2-inconsistent calibration. This L 2-inconsistency can be remedied by modifying the original estimation procedure. A novel calibration method, called the L 2 calibration, is proposed and proven to be L 2-consistent and enjoys optimal convergence rate. Furthermore a numerical example and some mathematical analysis are used to illustrate the source of the L 2-inconsistency problem.

Authors:
 [1];  [2]
  1. Chinese Academy of Sciences (CAS), Beijing (China)
  2. Georgia Inst. of Technology, Atlanta, GA (United States)
Publication Date:
Research Org.:
Georgia Tech Research Corp., Atlanta, GA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
OSTI Identifier:
1405142
Report Number(s):
DOE-GT-0010548-2
Journal ID: ISSN 2166-2525; FG02-13ER26159
Grant/Contract Number:  
SC0010548
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
SIAM/ASA Journal on Uncertainty Quantification
Additional Journal Information:
Journal Volume: 4; Journal Issue: 1; Journal ID: ISSN 2166-2525
Publisher:
SIAM
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; computer experiments; uncertainty quantification; Gaussian process; reproducing kernel Hilbert space

Citation Formats

Tuo, Rui, and Jeff Wu, C. F. A Theoretical Framework for Calibration in Computer Models: Parametrization, Estimation and Convergence Properties. United States: N. p., 2016. Web. doi:10.1137/151005841.
Tuo, Rui, & Jeff Wu, C. F. A Theoretical Framework for Calibration in Computer Models: Parametrization, Estimation and Convergence Properties. United States. doi:10.1137/151005841.
Tuo, Rui, and Jeff Wu, C. F. Tue . "A Theoretical Framework for Calibration in Computer Models: Parametrization, Estimation and Convergence Properties". United States. doi:10.1137/151005841. https://www.osti.gov/servlets/purl/1405142.
@article{osti_1405142,
title = {A Theoretical Framework for Calibration in Computer Models: Parametrization, Estimation and Convergence Properties},
author = {Tuo, Rui and Jeff Wu, C. F.},
abstractNote = {Calibration parameters in deterministic computer experiments are those attributes that cannot be measured or available in physical experiments. Here, an approach to estimate them by using data from physical experiments and computer simulations. A theoretical framework is given which allows us to study the issues of parameter identifiability and estimation. We define the L2-consistency for calibration as a justification for calibration methods. It is shown that a simplified version of the original KO method leads to asymptotically L2-inconsistent calibration. This L2-inconsistency can be remedied by modifying the original estimation procedure. A novel calibration method, called the L2 calibration, is proposed and proven to be L2-consistent and enjoys optimal convergence rate. Furthermore a numerical example and some mathematical analysis are used to illustrate the source of the L2-inconsistency problem.},
doi = {10.1137/151005841},
journal = {SIAM/ASA Journal on Uncertainty Quantification},
issn = {2166-2525},
number = 1,
volume = 4,
place = {United States},
year = {2016},
month = {7}
}

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

Citation Metrics:
Cited by: 7 works
Citation information provided by
Web of Science

Save / Share: