Higher-order equivalent source decomposition using physics-informed learning for soundfield reconstruction

A wide range of spatial audio applications, including virtual navigation, immersive telepresence, and spatial noise control, require accurate and efficient emulation of room acoustics. Soundfield modeling using plane-wave and spherical-wave-based Equivalent Source Decomposition (ESD) provides a foundational framework for this task. However, the performance of these models is often constrained by the number and spatial distribution of available microphones, especially in reverberant environments. In this work, we propose a novel modeling framework based on higher-order equivalent sources, where both the spatial locations and order-dependent weights of the sources are estimated through a learning architecture that embeds the wave equation solution. This integration enables physically consistent and interpretable modeling of arbitrary soundfields from limited microphone observations. The effectiveness of the proposed method is demonstrated through a soundfield reconstruction problem, where it significantly outperforms both its omnidirectional counterpart and existing ESD variants.