  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.
