Sequential adaptive design for emulating costly computer codes

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 a challenging task. We address this problem by suggesting a novel adaptive sampling criterion called VIGF (variance of improvement for global fit). It is the variance of an improvement function which is defined at any location as the square of the difference between the fitted GP emulator and the model output at the nearest site in the current design. At each iteration of the proposed algorithm, a new run is performed where the VIGF criterion is the largest. Then, the new sample is added to the design and the emulator is updated accordingly. The batch version of VIGF is also proposed which can save the user time when parallel computing is available. The applicability of our method is assessed on a number 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 benchmarking functions in most cases.