Sound field reconstruction using a compact acoustics-informed neural network

Sound field reconstruction (SFR) augments the information of a sound field captured by a microphone array. Using basis function decomposition, conventional SFR methods 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 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. Experiments with acoustic transfer functions measured in different environments demonstrate the superiority of the AINN method over the traditional cylindrical harmonics and singular value decomposition methods.