Sound Field Reconstruction Using a Compact Acoustics-informed Neural Network

TL;DR

This paper introduces a compact acoustics-informed neural network (AINN) for sound field reconstruction that leverages the Helmholtz equation to produce physically valid and robust sound field estimates from limited measurements.

Contribution

The paper presents a novel neural network architecture that incorporates the Helmholtz equation, improving robustness and physical validity in sound field reconstruction compared to existing data-driven methods.

Findings

AINN outperforms traditional methods like cylinder harmonic decomposition.

The method accurately predicts sound pressures and gradients.

Numerical experiments validate the robustness and effectiveness of AINN.

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.