Abstract
First-order Ambisonics (FOA) is a standard spatial audio format based on spherical harmonic decomposition. Its zeroth- and first-order components capture the sound pressure and particle velocity, respectively. Recently, physics-informed neural networks have been applied to the spatial interpolation of FOA signals, regularizing the network outputs based on soft penalty terms derived from physical principles, e.g., the linearized momentum equation. In this paper, we reformulate the task so that the predicted FOA signal automatically satisfies the linearized momentum equation. Our network approximates a scalar function called velocity potential, rather than the FOA signal itself. Then, the FOA signal can be readily recovered through the partial derivatives of the velocity potential with respect to the network inputs (i.e., time and microphone position) according to physics of sound propagation. By deriving the four channels of FOA from the single-channel velocity potential, the reconstructed signal follows the physical principle at any time and position by construction. Experimental results on room impulse response reconstruction confirm the effectiveness of the proposed framework.
Abstract (translated)
一阶Ambisonics（FOA）是一种基于球谐分解的标准空间音频格式，其零阶与一阶分量分别捕捉声压与质点速度。近期，物理信息神经网络已被应用于FOA信号的空间插值，通过基于物理原理（如线性化动量方程）推导的软惩罚项对网络输出进行正则化。本文重构了该任务，使预测的FOA信号自动满足线性化动量方程。我们的网络不直接预测FOA信号本身，而是近似一个称为速度势函数的标量函数。随后，根据声传播物理原理，FOA信号可通过速度势函数关于网络输入（即时间与麦克风位置）的偏导数直接恢复。通过从单通道速度势函数推导出FOA的四通道信号，重构的信号在构造上即遵循任意时间与位置的物理原理。关于房间脉冲响应重建的实验结果验证了所提框架的有效性。
URL
https://arxiv.org/abs/2603.22589
