Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 395, Issue -, Pages 410-431Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2019.06.041
Keywords
Physics-informed; Gaussian process regression; CoKriging; Multifidelity; Active learning; Error bound
Funding
- U.S. Department of Energy (DOE), Office of Science, Office of Advanced Scientific Computing Research (ASCR) as part of the Uncertainty Quantification in Advection-Diffusion-Reaction Systems [DE-AC05-76RL01830]
- DOE [DE-AC05-76RL01830]
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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 high-fidelity data using a parameterized GP with hyperparameters identified via optimization. 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 efficiency 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. (C) 2019 Published by Elsevier Inc.
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