Gaussian Process structure for the emulation of deterministic and stochastic solvers: a simulation study

The increased diffusion of complex numerical solvers to emulate physical processes demands the development of fast and accurate surrogate models. Gaussian Processes (GPs) are the most widely adopted models in this context, as they proved to be sufficiently flexible to effectively mimic the behaviour of complex phenomena and they also provide a quantification of uncertainty of predictions. However, the accuracy of the model depends on both the trend component and covariance structure. In this work we conduct an extensive simulation study that investigates the performance of several GP structures considering the deterministic, homoscedastic and heteroscedastic noise settings. As a result, the findings of this work provide guidelines to practitioners dealing with both deterministic and stochastic solvers.