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：本研究设计了一种基于物理信息神经网络（PINN）的框架，用于求解波动方程以实现声学共振分析。所提出的分析模型ResoNet通过最小化周期解损失函数与传统PINN损失函数，在执行共振分析的同时有效利用了神经网络的函数逼近能力。此外，该模型可便捷地应用于反问题。针对一维声管中的共振现象，通过含能量损失项波动方程的正向与逆向分析验证了所提方法的有效性。在正向分析中，通过有限差分法对比评估了PINN在共振问题中的适用性。逆向分析包括识别波动方程中的能量损失项及声管设计优化，均获得了良好的精度。