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

arXiv: https://arxiv.org/abs/2512.06417 · HTML: https://mlsanity.com/paper/2512.06417/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 38 references that are in the map.
- First posted on arXiv 6 Dec 2025.

## Builds on (most cited first, 16 of 16)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Transformer for Partial Differential Equations' Operator Learning](https://mlsanity.com/paper/2205.13671/) (2022)
- [Neural Operators for Accelerating Scientific Simulations and Design](https://mlsanity.com/paper/2309.15325/) (2023)
- [Towards Multi-spatiotemporal-scale Generalized PDE Modeling](https://mlsanity.com/paper/2209.15616/) (2022)
- [Sobolev Training for Neural Networks](https://mlsanity.com/paper/1706.04859/) (2017)
- [Seismic wave propagation and inversion with Neural Operators](https://mlsanity.com/paper/2108.05421/) (2021)
- [Physics-Informed Neural Network for Volumetric Sound field Reconstruction of Speech Signals](https://mlsanity.com/paper/2403.09524/) (2024)

## Built on by (most cited first, 2 of 2)

- [APEX: Amplitude Anchors and Phase Priors for Target-Scarce Higher-Frequency Wave Prediction](https://mlsanity.com/paper/2605.26732/) (2026)
- [Mitigating Spectral Bias in Neural Operators for Underwater Transmission Loss Prediction](https://mlsanity.com/paper/2608.18141/) (2026)

## Abstract (arXiv)

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.