用神经网络实现声场跨区域连续重建，兼顾物理规律与位置无关性。
Permutation-Invariant Physics-Informed Neural Network for Region-to-Region Sound Field Reconstruction
- 采用无序集合结构处理声源与接收区位置，支持任意排列输入。
- 融合亥姆霍兹方程作为物理约束，提升预测结果的物理一致性。
- 适用于真实场景中声源与麦克风位置连续变化的复杂声场重建。
现有声场重建方法多针对固定位置声源到接收区域的点对区域重建，通过插值声学传递函数（ATFs）实现。但现实中ATFs随声源和接收区域位置连续变化，现有方法适用性受限。本文提出一种排列不变的物理信息神经网络，用于跨区域声场重建，可对连续变化的声源与测量区域间ATFs进行插值。该方法采用深度集架构处理声源与接收区位置为无序集合，保持声学互易性；同时引入亥姆霍兹方程作为物理约束，指导网络训练，确保预测结果符合物理规律。
原文摘要 · Abstract (English)
Most existing sound field reconstruction methods target point-to-region reconstruction, interpolating the Acoustic Transfer Functions (ATFs) between a fixed-position sound source and a receiver region. The applicability of these methods is limited because real-world ATFs tend to varying continuously with respect to the positions of sound sources and receiver regions. This paper presents a permutation-invariant physics-informed neural network for region-to-region sound field reconstruction, which aims to interpolate the ATFs across continuously varying sound sources and measurement regions. The proposed method employs a deep set architecture to process the receiver and sound source positions as an unordered set, preserving acoustic reciprocity. Furthermore, it incorporates the Helmholtz equation as a physical constraint to guide network training, ensuring physically consistent predictions.
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