Neural networks have emerged as a tool for solving differential equations in many branches of engineering and science. But their progress in frequency domain acoustics is limited by the vanishing gradient problem that occurs at higher frequencies. This paper discusses a formulation that can address this issue. The problem of solving the governing differential equation along with the boundary conditions is posed as an unconstrained optimization problem. The acoustic field is approximated to the output of a neural network which is constructed in such a way that it always satisfies the boundary conditions. The applicability of the formulation is demonstrated on popular problems in plane wave acoustic theory. The predicted solution from the neural network formulation is compared with those obtained from the analytical solution. A good agreement is observed between the two solutions. The method of transfer learning to calculate the particle velocity from the existing acoustic pressure field is demonstrated with and without mean flow effects. The sensitivity of the training process to the choice of the activation function and the number of collocation points is studied.

翻译：神经网络已成为工程和科学多个分支中求解微分方程的工具。但在频域声学领域，其进展受到高频情况下出现的梯度消失问题的限制。本文探讨了一种能够解决该问题的公式化方法。将控制微分方程与边界条件联立求解的问题转化为无约束优化问题。通过构造一个始终满足边界条件的神经网络，将其输出近似为声场。该公式化方法在平面波声学理论的经典问题上得到验证，其预测解与解析解进行了对比，两者吻合良好。基于迁移学习技术，本文展示了在存在与不存在平均流效应的情况下，利用现有声压场计算质点速度的方法。同时研究了训练过程对激活函数选择及配点数量的敏感性。