Physics-informed neural networks in support of modal wavenumber estimation

A physics-informed neural network (PINN) enables the estimation of horizontal modal wavenumbers using ocean pressure data measured at multiple ranges. Mode representations for the ocean acoustic pressure field are derived from the Hankel transform relationship between the depth-dependent Green's function in the horizontal wavenumber domain and the field in the range domain. We obtain wavenumbers by transforming the range samples to the wavenumber domain, and maintaining range coherence of the data is crucial for accurate wavenumber estimation. In the ocean environment, the sensitivity of phase variations in range often leads to degradation in range coherence. To address this, we propose using OceanPINN [Yoon, Park, Gerstoft, and Seong, J. Acoust. Soc. Am. 155(3), 2037-2049 (2024)] to manage spatially non-coherent data. OceanPINN is trained using the magnitude of the data and predicts phase-refined data. Modal wavenumber estimation methods are then applied to this refined data, where the enhanced range coherence results in improved accuracy. Additionally, sparse Bayesian learning, with its high-resolution capability, further improves the modal wavenumber estimation. The effectiveness of the proposed approach is validated through its application to both simulated and SWellEx-96 experimental data.