# Physics-informed neural operators for the in situ characterization of locally reacting sound absorbers

arXiv: https://arxiv.org/abs/2604.07412 · HTML: https://mlsanity.com/paper/2604.07412/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 61 references that are in the map.
- First posted on arXiv 8 Apr 2026.

## Builds on (most cited first, 15 of 15)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [Neural Operators for Accelerating Scientific Simulations and Design](https://mlsanity.com/paper/2309.15325/) (2023)
- [Applications of physics informed neural operators](https://mlsanity.com/paper/2203.12634/) (2022)
- [Sound propagation in realistic interactive 3D scenes with parameterized sources using deep neural operators](https://mlsanity.com/paper/2308.05141/) (2023)
- [Room impulse response reconstruction with physics-informed deep learning](https://mlsanity.com/paper/2401.01206/) (2024)
- [Physics-informed neural networks for one-dimensional sound field predictions with parameterized sources and impedance boundaries](https://mlsanity.com/paper/2109.11313/) (2021)
- [Physics and geometry informed neural operator network with application to acoustic scattering](https://mlsanity.com/paper/2406.03407/) (2024)
- [A data-driven two-microphone method for in-situ sound absorption measurements](https://mlsanity.com/paper/2502.04143/) (2025)
- [In situ estimation of the acoustic surface impedance using simulation-based inference](https://mlsanity.com/paper/2509.08873/) (2025)
- [Surface impedance inference via neural fields and sparse acoustic data obtained by a compact array](https://mlsanity.com/paper/2602.11425/) (2026)

## Abstract (arXiv)

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.