Advances in the Design of Gaussian Processes as Surrogate Models for Computer Experiments

We present some advances in the design of computer experiments. A Gaussian Process (GP) model is fitted to the computer experiment data as a surrogate model. We investigate using the Active Learning (AL) strategy of finding design points that maximize reduction on predictive variance. Using a series of approximations based on standard results from linear algebra (Weyl’s inequalities) we establish a score that approximates the AL utility. Our method is illustrated with a simulated example as well as with an intermediate climate computer model. The second example requires the calibration of a model that depends on three parameters that summarize important climate properties. The calibration of the model is done using one observation derived from historical records and model runs on a grid of 426 different parameter combinations. We use our score to revisit this design and also explore the possibility of weighting the score to create more adequate designs in terms of the calibration problem at hand.