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Title: When Bifidelity Meets CoKriging: An Efficient Physics-Informed Multifidelity Method

Abstract

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 the GP as well. We prove that the resulting posterior mean by the new physics-informed approach preserves linear physical constraints up to an error bound. By using this method, we can obtain an accurate construction of a state of interest based on a partially correct physical model and a few accurate observations. We present numerical examples to demonstrate performance of the method.

Authors:
ORCiD logo [1];  [2];  [1]
  1. BATTELLE (PACIFIC NW LAB)
  2. University of Iowa
Publication Date:
Research Org.:
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1634211
Report Number(s):
PNNL-SA-140016
DOE Contract Number:  
AC05-76RL01830
Resource Type:
Journal Article
Journal Name:
SIAM Journal on Scientific Computing
Additional Journal Information:
Journal Volume: 42; Journal Issue: 1
Country of Publication:
United States
Language:
English

Citation Formats

Yang, Xiu, Zhu, Xueyu, and Li, Jing. When Bifidelity Meets CoKriging: An Efficient Physics-Informed Multifidelity Method. United States: N. p., 2020. Web. doi:10.1137/18M1231353.
Yang, Xiu, Zhu, Xueyu, & Li, Jing. When Bifidelity Meets CoKriging: An Efficient Physics-Informed Multifidelity Method. United States. https://doi.org/10.1137/18M1231353
Yang, Xiu, Zhu, Xueyu, and Li, Jing. Tue . "When Bifidelity Meets CoKriging: An Efficient Physics-Informed Multifidelity Method". United States. https://doi.org/10.1137/18M1231353.
@article{osti_1634211,
title = {When Bifidelity Meets CoKriging: An Efficient Physics-Informed Multifidelity Method},
author = {Yang, Xiu and Zhu, Xueyu and Li, Jing},
abstractNote = {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 the GP as well. We prove that the resulting posterior mean by the new physics-informed approach preserves linear physical constraints up to an error bound. By using this method, we can obtain an accurate construction of a state of interest based on a partially correct physical model and a few accurate observations. We present numerical examples to demonstrate performance of the method.},
doi = {10.1137/18M1231353},
url = {https://www.osti.gov/biblio/1634211}, journal = {SIAM Journal on Scientific Computing},
number = 1,
volume = 42,
place = {United States},
year = {2020},
month = {1}
}