Engineers widely use Gaussian process regression framework to construct surrogate models aimed to replace computationally expensive physical models while exploring design space. Thanks to Gaussian process properties we can use both samples generated by a high fidelity function (an expensive and accurate representation of a physical phenomenon) and a low fidelity function (a cheap and coarse approximation of the same physical phenomenon) while constructing a surrogate model. However, if samples sizes are more than few thousands of points, computational costs of the Gaussian process regression become prohibitive both in case of learning and in case of prediction calculation. We propose two approaches to circumvent this computational burden: one approach is based on the Nystr\"om approximation of sample covariance matrices and another is based on an intelligent usage of a blackbox that can evaluate a~low fidelity function on the fly at any point of a design space. We examine performance of the proposed approaches using a number of artificial and real problems, including engineering optimization of a rotating disk shape.
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