In this paper we propose the use of neural networks to predict the sound absorption coefficient spectra of finite porous samples with microphone arrays. The main goal is to train a model that can effectively mitigate the errors caused by the finite size effect. A convolutional neural network architecture is used to map the array data to the absorption coefficient at five frequencies. The training, validation and test data are numerically produced with a boundary element method; modelling a baffled, locally reacting porous absorber on a rigid backing with a Delany–Bazley–Miki model, for varying sample size, thickness, flow resistivity, incidence angle and frequency. The strength of using machine learning in this context is that no hypotheses are made about the sound field or the absorber, as the networks learn the necessary relationships from the data. We show that the network approximates well the absorption coefficient, as if the sample was infinite, in a wide range of cases.