Learning from data-driven sound field estimation using complex-valued neural networks

This paper explores the use of a complex-valued neural network for virtual sensing applications. The aim is to estimate the pressures from single frequency plane waves from various directions at control points where physical microphone measurements are not feasible. Making use of measurements from a microphone array arranged on an open sphere, the proposed network is trained to infer the spatial properties of sound fields, predicting the pressure at designated virtual sensor locations. A key contribution of this work is the analysis of the network’s internal operations via singular value decomposition (SVD) of its weight matrices. This analysis reveals how the captured sound fields are spatially encoded by the hidden layer, which can be considered as a pre-processing step. Different network configurations and training scenarios will be investigated, focusing on examining the spatial filtering performed by the hidden layer. The results not only demonstrate the potential of complex-valued neural networks in the context of virtual acoustic sensing but also provide valuable insights into its decision-making process.