Relative entropy of machine-learning for long-range sound propagation

Abstract

Machine-learning algorithms can provide fast surrogate models when trained on sampled predictions from physics-based numerical models. However, it is unknown whether surrogate data generated from propagation through single realizations of atmospheric turbulence, or from an ensemble of multiple realizations of turbulence, is most suitable for machine-learning models. This study examines the use of a Crank-Nicholson parabolic equation (CNPE) for generating surrogate data, and Latin hypercube sampling for the CNPE input. Two separate datasets are generated for 5000 samples of governing parameters. In the first dataset, each transmission loss field is computed for a single realization of turbulence, whereas the second uses transmission loss from an ensemble of 64 realizations. Errors for various machine learning approaches are evaluated against experimental observations of long-range (out to 8 km) sound propagation. Between experimental and surrogate differences in transmission loss at four ranges, the average deviation from zero relative entropy was quantified. As a measure of dissimilarity between two distributions it is 0.17 for single realizations of turbulence, and 0.29 for 64 realizations of turbulence. Surrogate data generated from single realizations of turbulence agree better with experimental data.