Jonas M. Schmid

Jonas M. Schmid, Johannes D. Schmid, Martin Eser et al.

Accurate knowledge of acoustic surface admittance or impedance is essential for reliable wave-based simulations, yet its in situ estimation remains challenging due to noise, model inaccuracies, and restrictive assumptions of conventional methods. This work presents a physics-informed neural operator approach for estimating frequency-dependent surface admittance directly from near-field measurements of sound pressure and particle velocity. A deep operator network is employed to learn the mapping from measurement data, spatial coordinates, and frequency to acoustic field quantities, while simultaneously inferring a globally consistent surface admittance spectrum without requiring an explicit forward model. The governing acoustic relations, including the Helmholtz equation, the linearized momentum equation, and Robin boundary conditions, are embedded into the training process as physics-based regularization, enabling physically consistent and noise-robust predictions while avoiding frequency-wise inversion. The method is validated using synthetically generated data from a simulation model for two planar porous absorbers under semi free-field conditions across a broad frequency range. Results demonstrate accurate reconstruction of both real and imaginary admittance components and reliable prediction of acoustic field quantities. Parameter studies confirm improved robustness to noise and sparse sampling compared to purely data-driven approaches, highlighting the potential of physics-informed neural operators for in situ acoustic material characterization.

Jonas M. Schmid, Johannes D. Schmid, Martin Eser et al.

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.