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

arXiv: https://arxiv.org/abs/2509.08873 · HTML: https://mlsanity.com/paper/2509.08873/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Sep 2025.

## Built on by (most cited first, 2 of 2)

- [Surface impedance inference via neural fields and sparse acoustic data obtained by a compact array](https://mlsanity.com/paper/2602.11425/) (2026)
- [Physics-informed neural operators for the in situ characterization of locally reacting sound absorbers](https://mlsanity.com/paper/2604.07412/) (2026)

## Abstract (arXiv)

Accurate acoustic simulations of enclosed spaces require precise boundary conditions, typically expressed through surface impedances for wave-based methods. Conventional measurement techniques often 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 acoustic surface impedances from sparse interior sound pressure measurements. The approach employs simulation-based inference, which leverages the expressiveness of modern 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 and further tested with impedance tube measurements used as reference, achieving robust and accurate estimation of all six individual impedances. Application to a numerical car cabin model further demonstrates reliable uncertainty quantification and high predictive accuracy even for complex-shaped geometries. Posterior predictive checks and coverage diagnostics confirm well-calibrated inference, highlighting the method's potential for generalizable, efficient, and physically consistent characterization of acoustic boundary conditions in real-world interior environments.