Efficient Emulators for Multivariate Deterministic Functions

One of the challenges with emulating the response of a multivariate function to its inputs is the quantity of data that must be assimilated, which is the product of the number of model evaluations and the number of outputs. This article shows how even large calculations can be made tractable. It is already appreciated that gains can be made when the emulator residual covariance function is treated as separable in the model-inputs and model-outputs. Here, an additional simplification on the structure of the regressors in the emulator mean function allows very substantial further gains. The result is that it is now possible to emulate rapidly—on a desktop computer—models with hundreds of evaluations and hundreds of outputs. This is demonstrated through calculating costs in floating-point operations, and in an illustration. Even larger sets of outputs are possible if they have additional structure, for example, spatial-temporal.