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

TL;DR

This paper introduces a permutation-invariant physics-informed neural network designed for region-to-region sound field reconstruction, effectively interpolating acoustic transfer functions across varying source and receiver positions while maintaining physical consistency.

Contribution

It proposes a novel deep set architecture combined with Helmholtz equation constraints to handle unordered positions and ensure physically accurate sound field predictions.

Findings

Achieves accurate interpolation of ATFs across varying positions

Maintains physical consistency through Helmholtz equation constraints

Outperforms traditional point-to-region methods in experiments

Abstract

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.