This study devised a physics-informed neural network (PINN) framework to solve the wave equation for acoustic resonance analysis. The proposed analytical model, ResoNet, minimizes the loss function for periodic solutions and 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. The resonance in a one-dimensional acoustic tube, and 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 via comparison with the finite-difference method. The inverse analysis, which included identifying the energy loss term in the wave equation and design optimization of the acoustic tube, was performed with good accuracy.

翻译：本研究设计了一种物理信息神经网络（PINN）框架，用于求解波动方程以进行声共振分析。所提出的分析模型ResoNet，通过最小化周期解损失函数和传统PINN损失函数，在利用神经网络函数逼近能力的同时有效执行共振分析。此外，该方法可便捷地应用于反问题。通过对含能量损耗项的波动方程进行正演与反演分析，验证了一维声学管中的共振现象及所提方法的有效性。在正演分析中，通过与有限差分法对比，评估了PINN对共振问题的适用性。反演分析则包括识别波动方程中的能量损耗项以及声学管的设计优化，均取得了良好的精度。