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Title: Physics-Informed CoKriging: A Gaussian-Process-Regression-Based Multifidelity Method for Data-Model Convergence

Abstract

In this work, we propose a new Gaussian process regression (GPR)-based multifidelity method: physics-informed CoKriging (CoPhIK). In CoKriging-based multifidelity methods, the quantities of interest are modeled as linear combinations of multiple parameterized stationary Gaussian processes (GPs), and the hyperparameters of these GPs are estimated from data via optimization. In CoPhIK, we construct a GP representing low-fidelity data using physics-informed Kriging (PhIK), and model the discrepancy between low- and highfidelity data using a parameterized GP with hyperparameters identified via optimization. Our approach reduces the cost of optimization for inferring hyperparameters by incorporating partial physical knowledge. We prove that the physical constraints in the form of deterministic linear operators are satisfied up to an error bound. Furthermore, we combine CoPhIK with a greedy active learning algorithm for guiding the selection of additional observation locations. The eciency and accuracy of CoPhIK are demonstrated for reconstructing the partially observed modified Branin function, reconstructing the sparsely observed state of a steady state heat transport problem, and learning a conservative tracer distribution from sparse tracer concentration measurements.

Authors:
ORCiD logo [1]; ORCiD logo [1];  [1];  [1]
  1. BATTELLE (PACIFIC NW LAB)
Publication Date:
Research Org.:
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1572472
Report Number(s):
PNNL-SA-139726
DOE Contract Number:  
AC05-76RL01830
Resource Type:
Journal Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 395
Country of Publication:
United States
Language:
English

Citation Formats

Yang, Xiu, Barajas-Solano, David A., Tartakovsky, Guzel D., and Tartakovsky, Alexandre M. Physics-Informed CoKriging: A Gaussian-Process-Regression-Based Multifidelity Method for Data-Model Convergence. United States: N. p., 2019. Web. doi:10.1016/j.jcp.2019.06.041.
Yang, Xiu, Barajas-Solano, David A., Tartakovsky, Guzel D., & Tartakovsky, Alexandre M. Physics-Informed CoKriging: A Gaussian-Process-Regression-Based Multifidelity Method for Data-Model Convergence. United States. doi:10.1016/j.jcp.2019.06.041.
Yang, Xiu, Barajas-Solano, David A., Tartakovsky, Guzel D., and Tartakovsky, Alexandre M. Tue . "Physics-Informed CoKriging: A Gaussian-Process-Regression-Based Multifidelity Method for Data-Model Convergence". United States. doi:10.1016/j.jcp.2019.06.041.
@article{osti_1572472,
title = {Physics-Informed CoKriging: A Gaussian-Process-Regression-Based Multifidelity Method for Data-Model Convergence},
author = {Yang, Xiu and Barajas-Solano, David A. and Tartakovsky, Guzel D. and Tartakovsky, Alexandre M.},
abstractNote = {In this work, we propose a new Gaussian process regression (GPR)-based multifidelity method: physics-informed CoKriging (CoPhIK). In CoKriging-based multifidelity methods, the quantities of interest are modeled as linear combinations of multiple parameterized stationary Gaussian processes (GPs), and the hyperparameters of these GPs are estimated from data via optimization. In CoPhIK, we construct a GP representing low-fidelity data using physics-informed Kriging (PhIK), and model the discrepancy between low- and highfidelity data using a parameterized GP with hyperparameters identified via optimization. Our approach reduces the cost of optimization for inferring hyperparameters by incorporating partial physical knowledge. We prove that the physical constraints in the form of deterministic linear operators are satisfied up to an error bound. Furthermore, we combine CoPhIK with a greedy active learning algorithm for guiding the selection of additional observation locations. The eciency and accuracy of CoPhIK are demonstrated for reconstructing the partially observed modified Branin function, reconstructing the sparsely observed state of a steady state heat transport problem, and learning a conservative tracer distribution from sparse tracer concentration measurements.},
doi = {10.1016/j.jcp.2019.06.041},
journal = {Journal of Computational Physics},
number = ,
volume = 395,
place = {United States},
year = {2019},
month = {10}
}