Hankel-FNO: Fast Underwater Acoustic Charting Via Physics-Encoded Fourier Neural Operator

TL;DR

Hankel-FNO addresses the need for scalable, real-time underwater acoustic charting by integrating physics-informed encodings of Hankel propagation and bathymetry into a Fourier Neural Operator. The method achieves higher accuracy than purely data-driven surrogates and substantially faster performance than traditional RAM solvers, with strong generalization across environments and sound-source configurations. A two-stage training/fine-tuning strategy enables rapid adaptation to new scenarios using limited data, and zero-shot high-resolution inference demonstrates discretization-invariance. These capabilities collectively position Hankel-FNO as a practical tool for environment-aware sensor placement and autonomous undersea navigation.

Abstract

Fast and accurate underwater acoustic charting is crucial for downstream tasks such as environment-aware sensor placement optimization and autonomous vehicle path planning. Conventional methods rely on computationally expensive while accurate numerical solvers, which are not scalable for large-scale or real-time applications. Although deep learning-based surrogate models can accelerate these computations, they often suffer from limitations such as fixed-resolution constraints or dependence on explicit partial differential equation formulations. These issues hinder their applicability and generalization across diverse environments. We propose Hankel-FNO, a Fourier Neural Operator (FNO)-based model for efficient and accurate acoustic charting. By incorporating sound propagation knowledge and bathymetry, our method has high accuracy while maintaining high computational speed. Results demonstrate that Hankel-FNO outperforms traditional solvers in speed and surpasses data-driven alternatives in accuracy, especially in long-range predictions. Experiments show the model's adaptability to diverse environments and sound source settings with minimal fine-tuning.

Figures (16)

• Figure 1: The architecture of Fourier neural operator. The detailed implementation is in Ref. [ li2020fourier ].
• Figure 2: The architecture of Hankel-FNO, where FNO serves as the backbone. Hankel function encoding and SSFs with bathymetry encoding are the input, and transmission losses are the output. In the context of acoustic charting, we mainly consider the variation in transmission losses with respect to range $r$ and depth $z$, so the spatial coordinate is defined as $x=(r,z)$.
• Figure 3: The training and fine-tuning strategy of Hankel-FNO. The model is initially trained on data with same source settings and similar bathymetry. For different scenarios, it is fine-tuned with a small amount of samples while maintaining accuracy. The cyan and purple squares denote the sound source positions of the training and fine-tuning data, respectively.
• Figure 4: SSF samples along the same bearing from different areas, where the first four are training data with similar bathymetry, and the last one is a fine-tuning sample with deeper bathymetry
• Figure 5: Standardized SSP samples at depth 700 m for four different bearings: $0^{\circ}$, $30^{\circ}$, $60^{\circ}$, and $90^{\circ}$, where $0^{\circ}$ corresponds to the eastward direction.