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Sound Field Reconstruction Using a Compact Acoustics-informed Neural Network

Fei Ma, Sipei Zhao, Ian S. Burnett

TL;DR

The paper addresses sound field reconstruction from boundary measurements by integrating physics with data-driven learning. It introduces a compact acoustics-informed neural network (AINN) regularized by the Helmholtz equation, capable of reconstructing both pressure and its gradient within a ROI. Compared to cylinder harmonics and SVD baselines, the AINN—especially the decoupled two-network design—delivers superior accuracy and robustness across multiple room environments and frequencies. This approach provides physically valid reconstructions with a lightweight model, offering practical benefits for real-time SFR and boundary-based field estimation in varied acoustic contexts.

Abstract

Sound field reconstruction (SFR) augments the information of a sound field captured by a microphone array. Conventional SFR methods using basis function decomposition are straightforward and computationally efficient, but may require more microphones than needed to measure the sound field. Recent studies show that pure data-driven and learning-based methods are promising in some SFR tasks, but they are usually computationally heavy and may fail to reconstruct a physically valid sound field. This paper proposes a compact acoustics-informed neural network (AINN) method for SFR, whereby the Helmholtz equation is exploited to regularize the neural network. As opposed to pure data-driven approaches that solely rely on measured sound pressures, the integration of the Helmholtz equation improves robustness of the neural network against variations during the measurement processes and prompts the generation of physically valid reconstructions. The AINN is designed to be compact, and is able to predict not only the sound pressures but also sound pressure gradients within a spatial region of interest based on measured sound pressures along the boundary. Numerical experiments with acoustic transfer functions measured in different environments demonstrate the superiority of the AINN method over the traditional cylinder harmonic decomposition and the singular value decomposition methods.

Sound Field Reconstruction Using a Compact Acoustics-informed Neural Network

TL;DR

The paper addresses sound field reconstruction from boundary measurements by integrating physics with data-driven learning. It introduces a compact acoustics-informed neural network (AINN) regularized by the Helmholtz equation, capable of reconstructing both pressure and its gradient within a ROI. Compared to cylinder harmonics and SVD baselines, the AINN—especially the decoupled two-network design—delivers superior accuracy and robustness across multiple room environments and frequencies. This approach provides physically valid reconstructions with a lightweight model, offering practical benefits for real-time SFR and boundary-based field estimation in varied acoustic contexts.

Abstract

Sound field reconstruction (SFR) augments the information of a sound field captured by a microphone array. Conventional SFR methods using basis function decomposition are straightforward and computationally efficient, but may require more microphones than needed to measure the sound field. Recent studies show that pure data-driven and learning-based methods are promising in some SFR tasks, but they are usually computationally heavy and may fail to reconstruct a physically valid sound field. This paper proposes a compact acoustics-informed neural network (AINN) method for SFR, whereby the Helmholtz equation is exploited to regularize the neural network. As opposed to pure data-driven approaches that solely rely on measured sound pressures, the integration of the Helmholtz equation improves robustness of the neural network against variations during the measurement processes and prompts the generation of physically valid reconstructions. The AINN is designed to be compact, and is able to predict not only the sound pressures but also sound pressure gradients within a spatial region of interest based on measured sound pressures along the boundary. Numerical experiments with acoustic transfer functions measured in different environments demonstrate the superiority of the AINN method over the traditional cylinder harmonic decomposition and the singular value decomposition methods.
Paper Structure (15 sections, 34 equations, 10 figures)

This paper contains 15 sections, 34 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Problem formulation
  3. Methodology
  4. The cylinder harmonics method
  5. The SVD method
  6. The acoustic-informed neural network method
  7. Experiments
  8. Data processing
  9. Implementation
  10. Performance metrics
  11. Sound pressure reconstruction: loudspeaker 7
  12. Sound pressure reconstruction: all loudspeakers
  13. Pressure gradient reconstruction: loudspeaker 7
  14. Pressure gradient reconstruction: all loudspeakers
  15. Conclusion

Figures (10)

  • Figure 1: (color online) Problem setup: A number of sources $\star$ generate a sound field within a ROI, which is measured by microphones $\bullet$ on the boundary of the ROI. The objective is to reconstruct the sound pressure and its gradient within the ROI based on the microphone measurement.
  • Figure 2: (color online) Architecture of the AINN: The inputs are Cartesian coordinates, and the outputs are the real and imaginary parts of the pressure reconstruction, denoted as $\mathcal{N}^{\Re}(x,y)$ and $\mathcal{N}^{\Im}(x,y)$, respectively. The data loss and the PDE loss are calculated with respect the pressure reconstructions and its Laplacian, respectively.
  • Figure 3: (color online) Experiment setup zhao2022room: the loudspeaker array and the microphone arrays.
  • Figure 4: (color online) Experiment setup: three room environments.
  • Figure 5: (color online) Pressure reconstruction: reconstruct the pressure within the planar array based on the measured pressure ($\star$) - Anechoic chamber.
  • ...and 5 more figures