Abstract
Neural networks constrained by the physical laws emerged as an alternate numerical tool. In this paper, the governing equation that represents the propagation of sound inside a one-dimensional duct carrying a heterogeneous medium is derived. The problem is converted into an unconstrained optimization problem and solved using neural networks. Both the acoustic state variables: acoustic pressure and particle velocity are predicted and validated with the traditional Runge-Kutta solver. The effect of the temperature gradient on the acoustic field is studied. Utilization of machine learning techniques such as transfer learning and automatic differentiation for acoustic applications is demonstrated.
Abstract (translated)
由物理定律约束的神经网络作为一种替代数值工具应运而生。本文推导了描述一维管道中携带非均匀介质内声波传播的控制方程，并将其转化为无约束优化问题，利用神经网络进行求解。文中预测并验证了声学状态变量（即声压和质点速度），并与传统的龙格-库塔(Runge-Kutta)方法进行了对比。研究还探讨了温度梯度对声场的影响。此外，展示了在声学应用中使用机器学习技术如迁移学习和自动微分的利用情况。
URL
https://arxiv.org/abs/2507.22370
