Modeling computer experiments with functional response

When conducting computer experiments, engineers frequently encounter functional data for which the response data are defined over an operating cycle, time, or spatial interval. There is little work in the literature to model functional response from computer experiment. In this paper, we propose functional linear model for the mean function in the Gaussian kriging model. We further propose a two-step estimation procedure for the functional linear model using penalized spline approach. The proposed approach is applied to the design of a valvetrain system.