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In this work, we propose a framework that combines theapproximation-theory-based multifidelity method andGaussian-process-regression-based multifidelity method to achieve data-modelconvergence when stochastic simulation models and sparse accurate observationdata are available. Specifically, the two types of multifidelity methods we useare the bifidelity and CoKriging methods. The new approach uses the bifidelitymethod to efficiently estimate the empirical mean and covariance of thestochastic simulation outputs, then it uses these statistics to construct aGaussian process (GP) representing low-fidelity in CoKriging. We also combinethe bifidelity method with Kriging, where the approximated empirical statisticsare used to construct the GP as well. We prove that the resulting posteriormean by the new physics-informed approach preserves linear physical constraintsup to an error bound. By using this method, we can obtain an accurateconstruction of a state of interest based on a partially correct physical modeland a few accurate observations. We present numerical examples to demonstrateperformance of the method.

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