Physics-informed neural networks for acoustic boundary admittance estimation

Acoustic simulations often face significant uncertainties due to limited knowledge of acoustic boundary conditions. While measuring the boundary admittance in situ is challenging in practical applications, numerical inverse methods can be used to characterize the boundary conditions based on sound pressure data. However, conventional inverse methods require a validated forward model and can become impractical for computationally expensive simulation models. Over the past years, machine learning approaches have emerged as promising methods for scientific computing and data-driven modeling. Physics-informed neural networks incorporate physical prior knowledge into a neural network by adding the residual of the underlying partial differential equation to the loss function. Training the neural network minimizes the loss function, allowing the network to learn a solution that not only fits the training data but also satisfies the corresponding boundary value problem. In this study, physics-informed neural networks are trained to learn the sound pressure solution within two numerical examples governed by the Helmholtz equation without explicitly specifying the boundary conditions at selected boundaries. After training, the neural network's prediction of the boundary admittance is evaluated and compared to the ground truth, initially assigned in the finite element reference solution. Additionally, the proposed method is validated using experimental data obtained from an acoustic impedance tube measurement. The results show that physics-informed neural networks can accurately learn the sound pressure field and implicitly solve the inverse problem by providing an accurate estimate of the underlying boundary admittance, even in the case of spatially varying boundary conditions.