This work describes an approach to aerodynamic shape design based on a multi-fidelity hierarchical structure in an evolutionary optimization context. In this procedure, the different levels of fidelity can be both physical models of varying accuracy solved numerically and surrogate models based on supervised or unsupervised machine-learning methodologies, but characterized by the fact that they use, both in training and in the generative phase, information coming from physical models. The basic idea is that of embedding physics information through multi-fidelity modeling in the approximators, i.e., inserting information on the physics of the problem using a low-fidelity model and ensuring that the approximator returns the difference between the low-fidelity model and the high-fidelity model. The availability of a hierarchy of increasingly complex solvers, namely a full potential with boundary layer correction and a Reynolds Averaged Navier-Stokes solver, is exploited to train a physically informed surrogate model that, in the generative phase during the optimization process, corrects the response of the low-order model in order to approximate the high fidelity one. The proposed approach aims to significantly reduce the database size needed to properly train an ML-based surrogate, balancing between the need for machine learning approaches to have an extensive database available for training and the need for design procedures to use the least possible number of high-fidelity evaluations.