The framework of this work is the optimisation of aero-acoustic noise reduction for Ultra High ByPass Ratio (UHBR) engines. Such an optimisation is done for low frequency tonal acoustic noises by means of tailored aero-acoustic liners. In order to avoid the prohibitively high computational and experimental costs for the design optimisation of these liners, a metamodel has to be constructed and is chosen as a neural network. In general big dataset is required for training the neural network. Since only small dataset is available, we propose to use a probabilistic learning tool for generating this big dataset and then training the neural network. For supervised or unsupervised cases, with or without constraints, Probabilistic Learning on Manifolds (PLoM) [1,2] is a machine-learning tool that allows a learned set to be generated from a given training set whose points are realisations of a non-Gaussian random vector whose support of its probability distribution is concentrated in a subset (a manifold). This approach allows for discovering the geometric properties of the probability measure support and preserves the concentration of the probability measure for the learned set. This approach has specifically been developed for the case of small training sets as opposed to big datasets. In a first step PLoM is used for constructing a probabilistic metamodel of aero-acoustic liner impedance for which a training set has been constructed with a high fidelity computational aero-acoustics (CAA) model [3]. Conditional statistics of the real and imaginary parts of the frequency dependent random impedance are estimated, which allows the metamodel to be constructed. This probabilistic metamodel is robust, has been validated though conditional statistics and measure of concentration. In the second step, this probabilistic metamodel is used as a generator to train an artificial neural network (ANN) [4] which will be inturn used for design optimisation. This ANN allows for predicting the mean value and the confidence region of the real and imaginary parts of the random impedance as a function of the frequency. [1] C. Soize, R. Ghanem, Probabilistic learning on manifolds, Foundations of Data Science, American Institute of Mathematical Sciences, 2 (3), 279-307, 2020, doi: 10.3934/fods.2020013. [2] C. Soize, R. Ghanem. Probabilistic learning on manifolds (PLoM) with partition, International Journal for Numerical Methods in Engineering, 123, 268-290, 2022, doi: 10.1002/nme.6856. [3] M, Lavieille, T. Abboud, A. Bennani, N. Balin, Numerical simulations of perforate liners: Part I – Model description and impedance validation, 19th AIAA/CEAS Aeroacoustics Conference, pp.2269, 2013, doi :10.2514/6.2013-2269. [4] M. H. Hassoun, et al , Fundamentals of artificial neural networks, MIT press, 1995.