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Engineering problems often involve data sources of variable fidelity withdifferent costs of obtaining an observation. In particular, one can use both acheap low fidelity function (e.g. a computational experiment with a CFD code)and an expensive high fidelity function (e.g. a wind tunnel experiment) togenerate a data sample in order to construct a regression model of a highfidelity function. The key question in this setting is how the sizes of thehigh and low fidelity data samples should be selected in order to stay within agiven computational budget and maximize accuracy of the regression model priorto committing resources on data acquisition.  In this paper we obtain minimax interpolation errors for single and variablefidelity scenarios for a multivariate Gaussian process regression. Evaluationof the minimax errors allows us to identify cases when the variable fidelitydata provides better interpolation accuracy than the exclusively high fidelitydata for the same computational budget.  These results allow us to calculate the optimal shares of variable fidelitydata samples under the given computational budget constraint. Real andsynthetic data experiments suggest that using the obtained optimal shares oftenoutperforms natural heuristics in terms of the regression accuracy.

Minimax Error of Interpolation and Optimal Design of Experiments for Variable Fidelity Data