HelmholtzNet: Physics-informed graph neural network for acoustic pressure estimation
We present a method for predicting the ocean acoustic pressure field from partially observed pressure magnitudes across range–depth locations. Our framework leverages a physics-informed graph neural network (PIGNN), in which graph connectivity encodes the local spatial structure of the waveguide and enables stable learning of highly oscillatory fields. The PIGNN is trained to map range and depth coordinates to complex acoustic pressure while enforcing the partial differential equation (PDE) governing underwater sound propagation. In large-scale environments, pressure fields often exhibit rapid phase fluctuations over kilometer-scale distances, even at frequencies below 100 Hz, leading to highly complex solution landscapes that standard neural networks struggle to approximate. A key contribution of this work is demonstrating that graph-based message passing, combined with the envelope function derived from the parabolic equation (PE) model, effectively mitigates this challenge by capturing local phase relationships and yielding a substantially smoother learning target. By jointly incorporating the governing PDE and the spatial structure of the environment, the PIGNN achieves accurate pressure predictions with limited training data and improved generalization. [Work supported by ONR (Code 322).]