Frequency-domain physics-informed neural network for accurate reconstruction of 3D acoustic fields under sparse and multi-frequency measurements

Accurate reconstruction of three-dimensional acoustic fields from sparse multi-frequency measurements is essential for engineering tasks such as cabin noise control, building-acoustics optimization, and machinery diagnostics. In this study, a frequency-domain physics-informed neural network (PINN) framework is presented, in which the inhomogeneous Helmholtz equation with an explicit monopole source term is embedded into the loss function so that phase-consistent and physically plausible predictions are enforced. To enhance broadband performance under sparse spatial sampling, a multi-branch network architecture with Fourier feature encoding is employed, by which frequency-specialized learning is enabled while model compactness is maintained. The proposed method is validated on a high-fidelity three-dimensional acoustic dataset under varying spatial sampling densities and frequency resolutions. Compared with both the homogeneous-PDE PINN and the purely data-driven baseline, our model reduces RMSE by up to 60 %. It also increases the correlation by 20-60 %across the evaluated frequencies and test sets. Results demonstrate that the PINN achieves superior reconstruction accuracy and generalization across the full frequency spectrum, significantly outperforming the baseline in sparse measurement scenarios. This study provides a data-efficient and physically consistent solution for broadband 3D acoustic field reconstruction.