Qiang Xi

Jiahao Li, Qiang Xi, Ilia Marchevskiy et al.

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.

Qiang Xi, Wenzhi Xu, Mario Cvetkovic et al.

We propose a localized physics-informed kernel function neural network (LPIKFNN), which is an improved physics-informed neural network (PINN) based on physics-informed kernel function (PIKF). In the LPIKFNN framework, the localized collocation scheme discretizes the physical quantities within the local domain, where the physical field is represented as a linear combination of PIKFs. Based on this representation, the multilayer perceptron is trained to iteratively learn the physical quantities. To overcome the computational challenges of conventional PINN in higher-order derivative and high wavenumber problems, the LPIKFNN constructs the loss function using the PIKF and a localized collocation scheme rather than relying on automatic differentiation. As a result, the costly derivative evaluations required to enforce governing equations during iterative training are eliminated, leading to significantly improved computational efficiency and training performance. Moreover, incorporating PIKFs into the loss function enables the proposed LPIKFNN to significantly improve computational accuracy in high-wavenumber problems characterized by highly oscillatory physical fields. To overcome the computational bottleneck of the physics-informed kernel function neural network (PIKFNN) in heterogeneous problems, the LPIKFNN introduces a localized collocation scheme that removes reliance on global PIKFs, enabling accurate predictions where global PIKFs are unavailable. The feasibility and accuracy of the proposed LPIKFNN are demonstrated through a series of benchmark studies, including high wavenumber problems, higher-order derivative problems, nonlinear problems, heterogeneous problems, and potential-based inverse electromyography. The numerical predictions obtained by LPIKFNN show excellent agreement with available analytical solutions and experimental measurements.