Explaining neural network predictions of acoustic fields in ideal single- and multi-path environments

Neural networks are an increasingly popular tool for solving a wide variety of problems. Given some up-front computational effort, the complex patterns which exist in large datasets can be embedded in an explicit, though difficult to interpret, neural-network ‘formula’ for future predictions. As reliance on neural networks increases, so does the demand for their explainability, since practitioners must create safe and unbiased methods. In this presentation, an effort is made to better explain and understand neural networks which are trained to provide solutions to the point-source Helmholtz-equation in axisymmetric single-path, two-path, and multi-path (ideal waveguide) environments having constant sound speed. This analysis emphasizes source frequencies in the 100s of Hz, depths up to 500 m, and ranges up to 1 km for sound speeds near 1500 m/s. In all cases, the neural networks' intermediate computational values are compared to those of the corresponding analytical Helmholtz-equation solution used to generate the neural networks' training dataset. The effects of the choice of neural network inputs, noise-like inputs, and correlated input features are also considered. The insights developed from this investigation provide insights for the extension of neural network predictions of acoustic fields to more complex environments. [Work supported by the NDSEG fellowship program.]