The main novelty of this paper consists in presenting a statistical Artificial Neural Network (ANN) based model for a robust prediction of the frequency-dependent aeroacoustic liner impedance using an Aeroacoustic Computational Model (ACM) dataset of small size. The model, focusing on Percentage of Open Area (POA) and Sound Pressure Level (SPL) at a zero Mach number, takes into accounts uncertainties using a probabilistic formulation. The main difficulty in training an ANN-based model is the small size of the ACM dataset. The probabilistic learning carried out using the Probabilistic Learning on Manifold (PLoM) algorithm addresses this difficulty as it allows constructing a very large training dataset from learning the probabilistic model from a small dataset. A prior conditional probability model is presented for the PCA-based statistical reduced representation of the frequency-sampled vector of the logresistance and reactance. It induces some statistical constraints that are not straightforwardly taken into account when training such an ANN-based model by classical optimizations methods under constraints. A second novelty of this paper consists in presenting an alternate solution that involves using conditional statistics estimated with learned realizations from PLoM. A numerical example is presented.