The use of surrogate models in recent times plays a key role in the design process and, over the past few years, machine learning algorithms are adapting to the use of active metamodelling techniques. In the present study, Artificial Neural Networks formulation is used as a data-driven nonlinear model aimed at describing the dynamics of an experimental test campaign related to the noise emitted by a single-stream jet in under-expanded conditions. The architecture of the neural network is selected employing a deterministic optimization algorithm, coupled with data informed tuning of the input parameters. The data set explored here was acquired in the state-of-the-art aeroacoustic facility at the University of Bristol. Both the near- and far-field acoustic measurements were carried out for a cold under-expanded jet for Mach numbers ranging from 1.1 to 1.4. The predictions by the metamodel are in good agreement with the experimental data, and the results demonstrate the capability of metamodels as a reliable tool to estimate jet noise in under-expanded flow conditions for a wide range of Mach numbers and near-field locations.