Identification of Physical Properties in Acoustic Tubes Using Physics-Informed Neural Networks

Physics-informed Neural Networks (PINNs) is a method for numerical simulation that incorporates a loss function corresponding to the governing equations into a neural network. While PINNs have been explored for their utility in inverse analysis, their application in acoustic analysis remains limited. This study presents a method to identify loss parameters in acoustic tubes using PINNs. We categorized the loss parameters into two groups: one dependent on the tube's diameter and another constant, independent of it. The latter were set as the trainable parameters of the neural network. The problem of identifying the loss parameter was formulated as an optimization problem, with the physical properties being determined through this process. The neural network architecture employed was based on our previously proposed ResoNet, which is designed for analyzing acoustic resonance. The efficacy of the proposed method is assessed through both forward and inverse analysis, specifically through the identification of loss parameters. The findings demonstrate that it is feasible to accurately identify parameters that significantly impact the sound field under analysis. By merely altering the governing equations in the loss function, this method could be adapted to various sound fields, suggesting its potential for broad application.

Physics-informed Neural Network for Acoustic Resonance Analysis

This study proposes the physics-informed neural network (PINN) framework to solve the wave equation for acoustic resonance analysis. ResoNet, the analytical model proposed in this study, minimizes the loss function for periodic solutions, in addition to conventional PINN loss functions, thereby effectively using the function approximation capability of neural networks, while performing resonance analysis. Additionally, it can be easily applied to inverse problems. Herein, the resonance in a one-dimensional acoustic tube was analyzed. The effectiveness of the proposed method was validated through the forward and inverse analyses of the wave equation with energy-loss terms. In the forward analysis, the applicability of PINN to the resonance problem was evaluated by comparison with the finite-difference method. The inverse analysis, which included the identification of the energy loss term in the wave equation and design optimization of the acoustic tube, was performed with good accuracy.