# Permutation-Invariant Physics-Informed Neural Network for Region-to-Region Sound Field Reconstruction

arXiv: https://arxiv.org/abs/2601.19491 · HTML: https://mlsanity.com/paper/2601.19491/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jan 2026.

## Built on by (most cited first, 1 of 1)

- [Optimal Transport-based Permutation-Invariant Bayesian Optimization of Offshore Wind Farm Layouts](https://mlsanity.com/paper/2606.00009/) (2026)

## Abstract (arXiv)

Most existing sound field reconstruction methods target point-to-region reconstruction, interpolating the Acoustic Transfer Functions (ATFs) between a fixed-position sound source and a receiver region. The applicability of these methods is limited because real-world ATFs tend to varying continuously with respect to the positions of sound sources and receiver regions. This paper presents a permutation-invariant physics-informed neural network for region-to-region sound field reconstruction, which aims to interpolate the ATFs across continuously varying sound sources and measurement regions. The proposed method employs a deep set architecture to process the receiver and sound source positions as an unordered set, preserving acoustic reciprocity. Furthermore, it incorporates the Helmholtz equation as a physical constraint to guide network training, ensuring physically consistent predictions.