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

TL;DR

This paper introduces a virtual boundary integral neural network (VBINN) for 3D exterior acoustic problems, combining boundary integral methods with neural networks to improve accuracy and stability.

Contribution

The paper proposes a novel VBINN approach that avoids singular kernel evaluations and optimizes virtual boundary parameters for enhanced 3D acoustic analysis.

Findings

VBINN achieves close agreement with analytical and COMSOL solutions.

The method effectively handles multiple bodies and underwater acoustic propagation.

The Burton Miller extension improves stability near characteristic frequencies.

Abstract

This paper presents a virtual boundary integral neural network (VBINN) for exterior acoustic problems in three dimensions. The method introduces a virtual boundary inside the scatterer or vibrating body and represents the associated source density with a neural network. Coupled with the acoustic fundamental solution, this representation satisfies the Sommerfeld radiation condition by construction 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 associated with coincident source and collocation points 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 exterior acoustic analysis in three dimensions.