Phase-Retrieval-Based Physics-Informed Neural Networks For Acoustic Magnitude Field Reconstruction

TL;DR

This work tackles estimating the acoustic magnitude field when phase measurements are unavailable. It introduces a phase-retrieval-based PINN that jointly learns magnitude $|u|$ and phase $\phi$ using two neural fields and enforces the Helmholtz PDE on the reconstructed complex amplitude $u = |u| e^{j\phi}$. The method leverages Random Fourier Features to capture high-frequency variations and trains on sparse magnitude data at multiple sensor locations. Experiments in simulated rooms show consistent performance gains over PDE-agnostic baselines, with stronger gains as more measurements are used and frequencies decrease, highlighting the importance of balanced physics and data losses.

Abstract

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.

Figures (6)

• Figure 1: Relationship of pressure fields and magnitude fields. The goal of our approach is to find a function which fulfills the two conditions, symbolised by the two circles.
• Figure 2: Visualization of our network architecture. Blue arrows highlight the data flow of the magnitude dataset, and red arrows of the reconstructed complex-valued pressure dataset.
• Figure 3: Experimental setup. Geometry of the room and target region $\Omega$.
• Figure 4: Plot of the test set data loss \ref{['eq:data_loss']} for different frequencies and numbers of sources in the training set. The use of the physics loss is beneficial in all cases.
• Figure 5: Visualization of the magnitude distribution in the $x$-$z$ plane at $200$ Hz and $400$ Hz.