Fast regression surrogates for computer models with time-dependent outputs

The study of physical processes is often aided by computer models or codes. Computer models that simulate such processes are sometimes computationally intensive and therefore not very efficient exploratory tools. In this paper, we address computer models characterized by temporal dynamics and propose new statistical correlation structures aimed at modelling their time dependence. These correlations are embedded in regression models with input-dependent design matrix and input-correlated errors that act as fast statistical surrogates for the computationally intensive dynamical codes. The methods are illustrated with an automotive industry application involving a road load data acquisition computer model.