用物理约束的边界积分网络，精准重建声场分布。
Sound Field Reconstruction Using Physics-Informed Boundary Integral Networks
- 基于基尔霍夫-赫姆霍兹方程构建边界积分网络
- 仅需少量麦克风测量点即可高精度还原声场
- 适合声学成像与低采样场景应用
声场重建旨在利用有限测量点估计任意空间区域的声压分布。现有方法多采用物理信息神经网络，在损失函数中引入亥姆霍兹或波动方程作为约束。本文提出一种边界积分网络，基于基尔霍夫-赫姆霍兹边界积分方程建模声场，通过浅层神经网络恢复域边界上的压力分布，从而精确推算内部声压。已知麦克风位置的前提下，模型通过最小化预测值与实测值间的均方误差进行训练。实验表明，该方法优于现有的物理信息数据驱动技术。
原文摘要 · Abstract (English)
Sound field reconstruction refers to the problem of estimating the acoustic pressure field over an arbitrary region of space, using only a limited set of measurements. Physics-informed neural networks have been adopted to solve the problem by incorporating in the training loss function the governing partial differential equation, either the Helmholtz or the wave equation. In this work, we introduce a boundary integral network for sound field reconstruction. Relying on the Kirchhoff-Helmholtz boundary integral equation to model the sound field in a given region of space, we employ a shallow neural network to retrieve the pressure distribution on the boundary of the considered domain, enabling to accurately retrieve the acoustic pressure inside of it. Assuming the positions of measurement microphones are known, we train the model by minimizing the mean squared error between the estimated and measured pressure at those locations. Experimental results indicate that the proposed model outperforms existing physics-informed data-driven techniques.
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