  Stochastic kriging has been widely employed for simulation metamodeling to
predict the response surface of complex simulation models. However, its use is
limited to cases where the design space is low-dimensional because, in general,
the sample complexity (i.e., the number of design points required for
stochastic kriging to produce an accurate prediction) grows exponentially in
the dimensionality of the design space. The large sample size results in both a
prohibitive sample cost for running the simulation model and a severe
computational challenge due to the need to invert large covariance matrices.
Based on tensor Markov kernels and sparse grid experimental designs, we develop
a novel methodology that dramatically alleviates the curse of dimensionality.
We show that the sample complexity of the proposed methodology grows only
slightly in the dimensionality, even under model misspecification. We also
develop fast algorithms that compute stochastic kriging in its exact form
without any approximation schemes. We demonstrate via extensive numerical
experiments that our methodology can handle problems with a design space of
more than 10,000 dimensions, improving both prediction accuracy and
computational efficiency by orders of magnitude relative to typical alternative
methods in practice.
