Range sampling strategies for statistical learning models in the context of long-range outdoor propagation

Long-range outdoor sound propagation is characterized by a large variance in sound pressure levels over space and time. While conventional numerical methods for long-range propagation capture this variability, they are costly in computational memory and time. In contrast statistical learning algorithms provide very fast predictions by learning from experimental observations, or surrogate data generated by a numerical method. However, a challenge in training with surrogate data is in selecting a sampling strategy for the numerical output. This study examines the use of a Crank-Nicholson parabolic equation (CNPE) for generating surrogate data, Latin hypercube sampling for the CNPE input, and three sampling strategies for the simulation output: randomly sample at a single range, sample at a discrete number of ranges, and randomly sample from a set of discrete ranges, all at a fixed receiver height. Consideration is given to ensemble decision trees, ensemble neural networks, and cluster-weighted models for nonlinear regression. By training an ensemble of decision trees with 5000 samples, and randomly sampling at a single range, the estimated overall test root-mean-square error between model predictions and CNPE predictions is 6.7 dB. Errors related to sampling strategies and modeling approaches are quantified in this study.