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In this work, we propose a new Gaussian process regression (GPR)-basedmultifidelity method: physics-informed CoKriging (CoPhIK). In CoKriging-basedmultifidelity methods, the quantities of interest are modeled as linearcombinations of multiple parameterized stationary Gaussian processes (GPs), andthe hyperparameters of these GPs are estimated from data via optimization. InCoPhIK, we construct a GP representing low-fidelity data using physics-informedKriging (PhIK), and model the discrepancy between low- and high-fidelity datausing a parameterized GP with hyperparameters identified via optimization. Ourapproach reduces the cost of optimization for inferring hyperparameters byincorporating partial physical knowledge. We prove that the physicalconstraints in the form of deterministic linear operators are satisfied up toan error bound. Furthermore, we combine CoPhIK with a greedy active learningalgorithm for guiding the selection of additional observation locations. Theefficiency and accuracy of CoPhIK are demonstrated for reconstructing thepartially observed modified Branin function, reconstructing the sparselyobserved state of a steady state heat transport problem, and learning aconservative tracer distribution from sparse tracer concentration measurements.

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