Classification tasks are frequent in many applications in science and engineering. A wide variety of statistical learning methods exists to deal with these problems. However, in many industrial applications, the number of available samples to train and construct a classifier is scarce and this has an impact on the classifications performances. In this work, we consider the case in which some a priori information on the system is available in form of a mathematical model. In particular, a set of numerical simulations of the system can be integrated to the experimental dataset. The main question we address is how to integrate them systematically in order to improve the classification performances. The method proposed is based on Nearest Neighbours and on the notion of Hausdorff distance between sets. Some theoretical results and several numerical studies are proposed.