# HergNet: a Fast Neural Surrogate Model for Sound Field Predictions via Superposition of Plane Waves

arXiv: https://arxiv.org/abs/2510.24279 · HTML: https://mlsanity.com/paper/2510.24279/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 30 references that are in the map.
- First posted on arXiv 28 Oct 2025.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Conservation Laws: A Divergence-Free Perspective](https://mlsanity.com/paper/2210.01741/) (2022)
- [Machine learning in acoustics: theory and applications](https://mlsanity.com/paper/1905.04418/) (2019)
- [Sound propagation in realistic interactive 3D scenes with parameterized sources using deep neural operators](https://mlsanity.com/paper/2308.05141/) (2023)
- [Physics-informed neural networks for one-dimensional sound field predictions with parameterized sources and impedance boundaries](https://mlsanity.com/paper/2109.11313/) (2021)
- [Physics-Informed Holomorphic Neural Networks (PIHNNs): Solving Linear Elasticity Problems](https://mlsanity.com/paper/2407.01088/) (2024)
- [A holomorphic Kolmogorov-Arnold network framework for solving elliptic problems on arbitrary 2D domains](https://mlsanity.com/paper/2507.22678/) (2025)

## Abstract (arXiv)

We present a novel neural network architecture for the efficient prediction of sound fields in two and three dimensions. The network is designed to automatically satisfy the Helmholtz equation, ensuring that the outputs are physically valid. Therefore, the method can effectively learn solutions to boundary-value problems in various wave phenomena, such as acoustics, optics, and electromagnetism. Numerical experiments show that the proposed strategy can potentially outperform state-of-the-art methods in room acoustics simulation, in particular in the range of mid to high frequencies.