Subsampling under distributional constraints

Some complex models are frequently employed to describe physical and mechanical phenomena. In this setting, we have an input in a general space, and an output where is a very complicated function, whose computational cost for every new input is very high, and may be also very expensive. We are given two sets of observations of , and of different sizes such that only is available. We tackle the problem of selecting a subset of smaller size on which to run the complex model , and such that the empirical distribution of is close to that of . We suggest three algorithms to solve this problem and show their efficiency using simulated datasets and the Airfoil self-noise data set.