Invertible neural networks for reconstructing acoustic fields

Abstract

Sound field reconstruction from finite measurement arrays provides a means to interpolate and extrapolate acoustic quantities that describe the field. By assuming a linear projection on a basis that follows a principled source propagation, one can recover accurate estimates of the aforementioned sound fields. However, the recovery of the basis coefficients relies on explicit models of which measurement noise and data incompleteness can profoundly affect the uncertainty of the solution. This work aims to estimate the distribution of the underlying pressure conditioned on the observations of the measured pressure in a room. A framework for approximate inference is adapted for sound field reconstruction by applying generative flow-based models and invertible neural network architectures. In particular, we use conditional normalising flows for fast conditional posterior estimation and uncertainty quantification. The model's evaluation is carried out using experimental data measured with a spherical array and compared to hierarchical Bayes with Markov Chain Monte-Carlo sampling.