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

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.