  Gaussian processes (GPs) are generally regarded as the gold standard
surrogate model for emulating computationally expensive computer-based
simulators. However, the problem of training GPs as accurately as possible with
a minimum number of model evaluations remains challenging. We address this
problem by suggesting a novel adaptive sampling criterion called VIGF (variance
of improvement for global fit). The improvement function at any point is a
measure of the deviation of the GP emulator from the nearest observed model
output. At each iteration of the proposed algorithm, a new run is performed
where VIGF is the largest. Then, the new sample is added to the design and the
emulator is updated accordingly. A batch version of VIGF is also proposed which
can save the user time when parallel computing is available. Additionally, VIGF
is extended to the multi-fidelity case where the expensive high-fidelity model
is predicted with the assistance of a lower fidelity simulator. This is
performed via hierarchical kriging. The applicability of our method is assessed
on a bunch of test functions and its performance is compared with several
sequential sampling strategies. The results suggest that our method has a
superior performance in predicting the benchmark functions in most cases.
