In situ estimation of the acoustic surface impedance using simulation-based inference

Accurate acoustic simulations of enclosed spaces require precise boundary conditions, typically expressed through surface impedances for wave-based methods. Conventional measurement techniques rely on simplifying assumptions about the sound field and mounting conditions, limiting their validity for real-world scenarios. To overcome these limitations, this study introduces a Bayesian framework for the in situ estimation of frequency-dependent surface impedances from sparse interior sound pressure measurements. The approach employs simulation-based inference, which leverages the expressiveness of neural network architectures to directly map simulated data to posterior distributions of model parameters, bypassing conventional sampling-based Bayesian approaches and offering advantages for high-dimensional inference problems. Impedance behavior is modeled using a damped oscillator model extended with a fractional calculus term. The framework is verified on a finite element model of a cuboid room with a volume of 1.95 m3 and further tested with impedance tube measurements used as reference, achieving robust and accurate estimation of all six individual impedances from 63 to 500 Hz. Application to a numerical car cabin model further demonstrates reliable uncertainty quantification and high predictive accuracy for complex-shaped geometries. Posterior predictive checks and coverage diagnostics confirm well-calibrated inference, highlighting the method's potential for generalizable and physically consistent characterization of acoustic boundary conditions in real-world interior environments.