Predicting ocean pressure field with a physics-informed neural network

Ocean sound pressure field prediction, based on partially measured pressure magnitudes at different range-depths, is presented. Our proposed machine learning strategy employs a trained neural network with range-depth as input and outputs complex acoustic pressure at the location. We utilize a physics-informed neural network (PINN), fitting sampled data while considering the additional information provided by the partial differential equation (PDE) governing the ocean sound pressure field. In vast ocean environments with kilometer-scale ranges, pressure fields exhibit rapidly fluctuating phases, even at frequencies below 100 Hz, posing a challenge for neural networks to converge to accurate solutions. To address this, we utilize the envelope function from the parabolic-equation technique, fundamental in ocean sound propagation modeling. The envelope function shows slower variations across ranges, enabling PINNs to predict sound pressure in an ocean waveguide more effectively. Additional PDE information allows PINNs to capture PDE solutions even with a limited amount of training data, distinguishing them from purely data-driven machine learning approaches that require extensive datasets. Our approach is validated through simulations and using data from the SWellEx-96 experiment.