A view on calibration and optimisation of computer models with Gaussian process emulators

Calibration of computer models aims to infer non-observable parameters of computational expensive and black-box computer codes from real observations. Bayesian calibration is a well established technique to obtain a posterior distribution over model parameters involving a model mismatch GP. Despite its appeal, the GP prior assumptions typically present a computational challenge due to the notoriously poor scalability of GPs. This approach is revisited employing low-rank GP approximations and stochastic variational inference techniques. Numerical experiments illustrate that the proposed approach enables a general and flexible framework for Bayesian calibration. Gaussian process models are also widely used in Bayesian optimisation. One of the most prominent approach for selecting a batch of evaluation points is based on the multipoint expected improvement criterion (EI). The computational burden of this selection rule is still an issue as the closed form formula of the multipoint EI relies on many calls of multivariate Gaussian cumulative distribution functions. Fast numerical approximations of the multipoint EI gradient  and efficient batch optimisation strategies will be presented.