Training physics-informed neural networks to directly predict acoustic field values in simple environments

As acousticians turn to machine learning for solutions to old and new problems, neural networks have become a go-to tool due to their capacity for model representation and quick forward computations. However, these benefits come at the cost of obscurity; it is difficult to determine whether the proficiency of a trained neural network is limited by training effort, training dataset size or scope, or compatibility of the network’s design with the data’s underlying pattern of interest. For neural networks trained to provide solutions to the point-source Helmholtz-equation in axisymmetric single-path, two-path, and multi-path (ideal waveguide) environments with constant sound speed, the key limitations are the dataset composition and network design. This study examines the effects on performance and explainablity which result from providing physical information (governing equation and boundary conditions) to these neural networks, instead of only acoustic-field solutions generated from well-known analytic solutions. The outcome of using physics-informed neural networks (PINNs) for these simple environments informs their possible extension to more complex, realistic environments. This study emphasizes source frequencies in the 100’s of Hz, depths up to 500 m, and ranges up to 10 km for sound speeds near 1500 m/s. [Work supported by the NDSEG fellowship program.]