Physics-Informed Neural Network-Driven Sparse Field Discretization Method for Near-Field Acoustic Holography

We propose the Physics-Informed Neural Network-driven Sparse Field Discretization method (PINN-SFD), a novel self-supervised, physics-informed deep learning approach for addressing the Near-Field Acoustic Holography (NAH) problem. Unlike existing deep learning methods for NAH, which are predominantly supervised by large datasets, our approach does not require a training phase and it is physics-informed. The wave propagation field is discretized into sparse regions, a process referred to as field discretization, which includes a series of set of source planes, to address the inverse problem. Our method employs the discretized Kirchhoff-Helmholtz integral as the wave propagation model. By incorporating virtual planes, additional constraints are enforced near the actual sound source, improving the reconstruction process. Optimization is carried out using Physics-Informed Neural Networks (PINNs), where physics-based constraints are integrated into the loss functions to account for both direct (from equivalent source plane to hologram plane) and additional (from virtual planes to hologram plane) wave propagation paths. Additionally, sparsity is enforced on the velocity of the equivalent sources. Our comprehensive validation across various rectangular and violin top plates, covering a wide range of vibrational modes, demonstrates that PINN-SFD consistently outperforms the conventional Compressive-Equivalent Source Method (C-ESM), particularly in terms of reconstruction accuracy for complex vibrational patterns. Significantly, this method demonstrates reduced sensitivity to regularization parameters compared to C-ESM.