We propose a method for estimating the magnitude distribution of an acoustic field from spatially sparse magnitude measurements. Such a method is useful when phase measurements are unreliable or inaccessible. Physics-informed neural networks (PINNs) have shown promise for sound field estimation by incorporating constraints derived from governing partial differential equations (PDEs) into neural networks. However, they do not extend to settings where phase measurements are unavailable, as the loss function based on the governing PDE relies on phase information. To remedy this, we propose a phase-retrieval-based PINN for magnitude field estimation. By representing the magnitude and phase distributions with separate networks, the PDE loss can be computed based on the reconstructed complex amplitude. We demonstrate the effectiveness of our phase-retrieval-based PINN through experimental evaluation.

翻译：我们提出了一种从空间稀疏幅值测量中估计声场幅值分布的方法。该方法在相位测量不可靠或无法获取时尤为有用。物理信息神经网络（PINNs）通过将控制偏微分方程（PDEs）导出的约束融入神经网络，已在声场估计中展现出潜力。然而，当相位测量缺失时，该方法无法直接应用，因为基于控制PDE的损失函数依赖于相位信息。为解决此问题，我们提出了一种基于相位恢复的PINN用于幅值场估计。通过使用独立的网络分别表示幅值和相位分布，可基于重建的复振幅计算PDE损失。我们通过实验评估验证了所提出的基于相位恢复的PINN的有效性。