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A methodology to learn acoustical responses based on limited experimental datasets is presented. From a methodological standpoint, the approach involves a multiscale-informed encoder used to cast the learning task in a finite-dimensional setting. A neural network model mapping parameters of interest to the latent variables is then constructed and calibrated using transfer learning and knowledge gained from the multiscale surrogate. The relevance of the approach is assessed by considering the prediction of the sound absorption coefficient for randomly-packed rigid spherical beads of equal diameter. A two-microphone method is used in this context to measure the absorption coefficient on a set of configurations with various monodisperse particle diameters and sample thicknesses, and a hybrid numerical approach relying on the Johnson-Champoux-Allard-Pride-Lafarge model is deployed as the multiscale-based predictor. It is shown that the strategy allows for the relationship between the micro-/structural parameters and the experimental acoustic response to be well approximated, even if a small physical dataset (comprised of ten samples) is used for training. The methodology, therefore, enables the identification and validation of acoustical models under constraints related to data limitation and parametric dependence. It also paves the way for an efficient exploration of the parameter space for acoustical materials design.