A fundamental problem in the applications involved with aerodynamic flows is the difficulty in finding a suitable dynamical model containing the most significant information pertaining to the physical system. Especially in the design of feedback control systems, a representative model is a necessary tool constraining the applicable forms of control laws. This article addresses the modelling problem by the use of feedforward neural networks (NNs). Shallow cavity flows at different Mach numbers are considered, and a single NN admitting the Mach number as one of the external inputs is demonstrated to be capable of predicting the floor pressures. Simulations and real time experiments have been presented to support the learning and generalization claims introduced by NN-based models.