Silvia Montagna (Duke University)

Computer emulation with non-stationary Gaussian processes

Computer codes are used widely in modern scientific research in complex chemical, thermodynamical and astrophysical processes. These codes deterministically map vectors of high-dimensional inputs into a scalar or vector-valued output, and must be run for many different input configurations to provide an adequate knowledge of the response surface. However, these computer models are very expensive to evaluate for all input values of interest. Therefore, there is often interest in building a statistical model also called “emulator” for the simulator itself, and the simulator deterministic output is regarded as a realization of a random function, typically a Gaussian process (GP).  A GP emulator run on finitely many input configurations offers error bars for response surface estimates at unseen input values. This helps identifying future input values where the experiments should be run to minimize the uncertainty in the response surface estimation. Literature on GP emulators focused primarily on stationary GPs, which however perform poorly when the surface of interest presents sharp features, such as abrupt discontinuities. We propose a simple non-stationary GP emulator, based on two stationary GPs, within a Bayesian framework,  and demonstrate its improved performance over stationary / treed GP emulators in learning anisotropic surfaces, dealing with discontinuities, identifying localized features in the response and increasing the sampling frequency in important input dimensions.