基于隐式神经表示与物理约束的室内声场重建方法

A Method for Indoor Sound Field Reconstruction Based on Implicit Neural Representations and Physical Constraints

摘要: 在实际室内声学应用中，受测点数量、布置条件及测量成本等因素限制，往往只能获得稀疏采样条件下的声场观测数据，给声场空间分布的准确重建带来挑战。针对这一问题，本文将室内稳态声场重建视为由空间坐标到声压幅值的函数拟合问题，提出一种融合隐式神经表示与物理约束的室内声场重建方法。该方法以多层感知机为基础，引入位置编码与正弦激活函数以增强网络对复杂空间振荡特征的表达能力，并进一步结合Helmholtz方程构建物理一致性约束，引导网络在稀疏采样条件下学习符合声波传播规律的声场空间分布。在不同采样率与频率条件下对所提方法进行了系统验证。实验结果表明，与传统MLP及仅引入位置编码的基线模型相比，该方法在稀疏采样条件下能够显著提升声场重建精度与稳定性，有效抑制未观测区域中的非物理振荡现象。相关研究为有限观测条件下的室内声场重建提供了一种可行的建模思路。

Abstract: In practical indoor acoustics applications, the number of measurement points is often limited by measurement conditions, sensor deployment, and acquisition costs, resulting in sparsely sampled sound field observations and posing challenges to accurate reconstruction of spatial sound field distributions. To address this problem, indoor steady-state sound field reconstruction is formulated as a function approximation task that maps spatial coordinates to sound pressure amplitudes. Based on this formulation, a sound field reconstruction method integrating implicit neural representations and physical constraints is proposed. The proposed method is built upon a multilayer perceptron architecture and incorporates positional encoding and sinusoidal activation functions to enhance the network’s capability in representing complex spatial oscillatory patterns. Furthermore, a physics-consistent constraint derived from the Helmholtz equation is introduced to guide the network toward learning sound field distributions that conform to acoustic wave propagation characteristics under sparse sampling conditions. The proposed method was systematically validated under different sampling rates and frequency conditions. The results demonstrate that, compared with conventional multilayer perceptron models and baseline models employing only positional encoding, the proposed method achieves higher reconstruction accuracy and improved stability under sparse sampling, while effectively suppressing non-physical oscillations in unobserved regions. The proposed approach provides a feasible modeling framework for indoor sound field reconstruction under limited observation conditions.