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

Xingyu Chen, Sipei Zhao, Fei Ma, Eva Cheng, Ian S. Burnett

TL;DR

The paper addresses region-to-region sound field reconstruction by interpolating Acoustic Transfer Functions across varying source and receiver positions. It introduces a permutation-invariant PINN (PI-PINN) that processes positions as an unordered set via a deep-set architecture and enforces physical consistency through a Helmholtz-based PDE loss. The approach yields reciprocal, physically plausible ATF predictions and demonstrates superior high-frequency performance compared with Kernel Ridge Regression on real-world data, with ablation confirming the necessity of both reciprocity-aware architecture and physics regularization. These results enable more robust and accurate region-to-region SFR in room acoustics and related applications, with future work aimed at complex indoor environments and environment priors.

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.

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

TL;DR

The paper addresses region-to-region sound field reconstruction by interpolating Acoustic Transfer Functions across varying source and receiver positions. It introduces a permutation-invariant PINN (PI-PINN) that processes positions as an unordered set via a deep-set architecture and enforces physical consistency through a Helmholtz-based PDE loss. The approach yields reciprocal, physically plausible ATF predictions and demonstrates superior high-frequency performance compared with Kernel Ridge Regression on real-world data, with ablation confirming the necessity of both reciprocity-aware architecture and physics regularization. These results enable more robust and accurate region-to-region SFR in room acoustics and related applications, with future work aimed at complex indoor environments and environment priors.

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.
Paper Structure (12 sections, 7 equations, 6 figures)

This paper contains 12 sections, 7 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Methodology
  4. Network Architecture for Permutation Invariance
  5. Physics-Informed Neural Network
  6. Implementation Remarks
  7. Experiments
  8. Dataset
  9. Ablation Study
  10. Results
  11. Conclusion
  12. Acknowledgments

Figures (6)

  • Figure 1: Conceptual diagram of Region-to-Region SFR.
  • Figure 2: Conceptual diagram of the proposed PI-PINN.
  • Figure 3: (a) Measurement setup from the UTS dataset, (b) Planar 64-microphone array.
  • Figure 4: NMSE (dB) as a function of frequency for four model variants in an anechoic room.
  • Figure 5: NMSE (dB) as a function of frequency for the proposed PI-PINN model and the KRR method.
  • ...and 1 more figures