  Many fields of science and engineering rely on running simulations with
complex and computationally expensive models to understand the involved
processes in the system of interest. Nevertheless, the high cost involved
hamper reliable and exhaustive simulations. Very often such codes incorporate
heuristics that ironically make them less tractable and transparent. This paper
introduces an active learning methodology for adaptively constructing surrogate
models, i.e. emulators, of such costly computer codes in a multi-output
setting. The proposed technique is sequential and adaptive, and is based on the
optimization of a suitable acquisition function. It aims to achieve accurate
approximations, model tractability, as well as compact and expressive simulated
datasets. In order to achieve this, the proposed Active Multi-Output Gaussian
Process Emulator (AMOGAPE) combines the predictive capacity of Gaussian
Processes (GPs) with the design of an acquisition function that favors sampling
in low density and fluctuating regions of the approximation functions.
Comparing different acquisition functions, we illustrate the promising
performance of the method for the construction of emulators with toy examples,
as well as for a widely used remote sensing transfer code.
