Physics-aware graph learning for sound-field reconstruction from sparse measurements

A graph neural network (GNN) framework is presented for reconstructing room-acoustic sound fields from sparse microphone measurements. Microphones, sources, and candidate field points are represented as a graph whose node and edge embeddings encode geometric priors and physics-aware features related to wave propagation. A principal neighbourhood aggregation architecture performs message passing and readout to estimate complex acoustic pressure at unobserved locations. Experiments on the MeshRIR dataset demonstrate robust reconstruction across a wide range of sampling sparsities and frequencies. Compared with cylindrical harmonics and plane wave expansion with regularized least squares, the proposed GNN yields consistently lower reconstruction error and higher spatial correlation, with gains most evident under very sparse sampling and at higher frequencies. These results indicate that graph-based learning, equipped with geometric and physics-aware representations, provides an effective and physically consistent approach to sound-field reconstruction for room acoustics.