Virtual boundary integral neural network for three-dimensional exterior acoustic problems

This paper presents a virtual boundary integral neural network (VBINN) for three-dimensional exterior acoustic problems. The method introduces a virtual boundary within the scatterer or vibrating body and represents the associated source density using a neural network. Based on the acoustic Green’s function, this representation satisfies the Sommerfeld radiation condition and enables direct evaluation of the acoustic pressure and its normal derivative at arbitrary field points. Because the integration surface is separated from the physical boundary, the formulation avoids the singular and near singular kernel evaluations in conventional boundary integral learning methods. To reduce sensitivity to boundary placement, the geometric parameters of the virtual boundary are optimized jointly with the source density during training. Numerical examples for acoustic scattering, multiple body interaction, and underwater acoustic propagation show close agreement with analytical solutions and COMSOL results, and the Burton-Miller extension further improves stability near characteristic frequencies. These results demonstrate the potential of VBINN for three-dimensional exterior acoustic analysis.