PhysicsInformed CoKriging: A GaussianProcessRegressionBased Multifidelity Method for DataModel Convergence
Abstract
In this work, we propose a new Gaussian process regression (GPR)based multifidelity method: physicsinformed CoKriging (CoPhIK). In CoKrigingbased 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 lowfidelity data using physicsinformed 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:

 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):
 PNNLSA139726
 DOE Contract Number:
 AC0576RL01830
 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, BarajasSolano, David A., Tartakovsky, Guzel D., and Tartakovsky, Alexandre M. PhysicsInformed CoKriging: A GaussianProcessRegressionBased Multifidelity Method for DataModel Convergence. United States: N. p., 2019.
Web. doi:10.1016/j.jcp.2019.06.041.
Yang, Xiu, BarajasSolano, David A., Tartakovsky, Guzel D., & Tartakovsky, Alexandre M. PhysicsInformed CoKriging: A GaussianProcessRegressionBased Multifidelity Method for DataModel Convergence. United States. doi:10.1016/j.jcp.2019.06.041.
Yang, Xiu, BarajasSolano, David A., Tartakovsky, Guzel D., and Tartakovsky, Alexandre M. Tue .
"PhysicsInformed CoKriging: A GaussianProcessRegressionBased Multifidelity Method for DataModel Convergence". United States. doi:10.1016/j.jcp.2019.06.041.
@article{osti_1572472,
title = {PhysicsInformed CoKriging: A GaussianProcessRegressionBased Multifidelity Method for DataModel Convergence},
author = {Yang, Xiu and BarajasSolano, 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: physicsinformed CoKriging (CoPhIK). In CoKrigingbased 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 lowfidelity data using physicsinformed 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}
}