Boundary integrated neural networks (BINNs) for acoustic radiation and scattering

TL;DR

This paper introduces boundary integrated neural networks (BINNs), a novel method that efficiently models acoustic radiation and scattering by embedding boundary integral equations into neural networks, achieving high accuracy with fewer data points.

Contribution

The paper proposes BINNs that incorporate boundary integral equations into neural networks, improving efficiency and accuracy for acoustic problems in unbounded domains.

Findings

BINNs require only boundary collocation points for input

BINNs converge faster than PINNs due to simpler loss functions

BINNs achieve comparable or better accuracy with fewer neurons

Abstract

This paper presents a novel approach called the boundary integrated neural networks (BINNs) for analyzing acoustic radiation and scattering. The method introduces fundamental solutions of the time-harmonic wave equation to encode the boundary integral equations (BIEs) within the neural networks, replacing the conventional use of the governing equation in physics-informed neural networks (PINNs). This approach offers several advantages. Firstly, the input data for the neural networks in the BINNs only require the coordinates of "boundary" collocation points, making it highly suitable for analyzing acoustic fields in unbounded domains. Secondly, the loss function of the BINNs is not a composite form, and has a fast convergence. Thirdly, the BINNs achieve comparable precision to the PINNs using fewer collocation points and hidden layers/neurons. Finally, the semi-analytic characteristic of the BIEs contributes to the higher precision of the BINNs. Numerical examples are presented to demonstrate the performance of the proposed method.