Reliable acoustic simulations of interior environments critically depend on accurate knowledge of the boundary conditions of all interacting surfaces. Phase information is crucial in the modal frequency range, yet it is not captured by the commonly used absorption coefficient. Therefore, the complex-valued surface impedance is used, which is typically measured under controlled laboratory conditions, such as the impedance tube. However, standardized setups fail to capture the complex acoustic behavior arising from real-world mounting conditions and realistic, non-planar sound fields, highlighting the need for in situ characterization techniques. In this contribution, we propose two machine learning-based approaches for estimating surface impedances directly from sound pressure measurements. The first is a Bayesian approach based on simulation-based inference, where a neural network is trained to approximate the posterior distribution of the unknown impedances. This approach is built upon a finite element model, making it particularly suitable for use in digital twins and model updating workflows where physics-based models already exist. The second method employs a Deep Operator Network to learn the mapping between sound pressure field and boundary conditions, offering a flexible alternative for impedance estimation. Both approaches are validated on representative problems, demonstrating their accuracy, robustness, and potential for real-world applications.
Schmid et al. (2025) studied this question.