Machine-learning of long-range sound propagation through simulated atmospheric turbulence

Conventional numerical methods can capture the inherent variability of long-range outdoor sound propagation. However, computational memory and time requirements are high. In contrast, machine-learning models provide very fast predictions. This comes by learning from experimental observations or surrogate data. Yet, it is unknown what type of surrogate data is most suitable for machine-learning. This study used a Crank-Nicholson parabolic equation (CNPE) for generating the surrogate data. The CNPE input data were sampled by the Latin hypercube technique. Two separate datasets comprised 5000 samples of model input. The first dataset consisted of transmission loss (TL) fields for single realizations of turbulence. The second dataset consisted of average TL fields for 64 realizations of turbulence. Three machine-learning algorithms were applied to each dataset, namely, ensemble decision trees, neural networks, and cluster-weighted models. Observational data come from a long-range (out to 8 km) sound propagation experiment. In comparison to the experimental observations, regression predictions have 5–7 dB in median absolute error. Surrogate data quality depends on an accurate characterization of refractive and scattering conditions. Predictions obtained through a single realization of turbulence agree better with the experimental observations.