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

2026-04-18

AI Summary

This work addresses the challenges of singularity, near-singularity, and enforcement of the Sommerfeld radiation condition in traditional boundary integral methods for three-dimensional exterior acoustic problems. The authors propose a novel approach that integrates a tunable virtual boundary within the scatterer with a physics-informed neural network to parameterize the source density. By leveraging the fundamental solution of acoustics, the method inherently satisfies the radiation condition and enables direct evaluation of acoustic pressure and its normal derivative at arbitrary field points. Singularities are eliminated by decoupling the integration surface from the physical boundary, while joint optimization of the virtual boundary geometry and source density enhances robustness. Furthermore, the Burton–Miller formulation is incorporated to improve numerical stability near characteristic frequencies. Numerical experiments demonstrate high accuracy and robustness in scenarios including acoustic scattering, multi-body coupling, and underwater sound propagation, with results in excellent agreement with analytical solutions and COMSOL simulations.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Large Multimodal Models (LMMs)
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Vertical and domain-specific search

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.

Problem

• exterior acoustic problems
• singular kernels
• boundary integral methods
• virtual boundary
• three-dimensional acoustics

Innovation

• virtual boundary
• boundary integral neural network
• exterior acoustics
• Sommerfeld radiation condition
• singular kernel avoidance