用神经网络预测变温变流速管道中的声场，物理约束提升精度。
Prediction of acoustic field in 1-D uniform duct with varying mean flow and temperature using neural networks
- 基于物理定律约束神经网络，求解一维管道声传播方程。
- 同时预测声压与质点速度，与经典数值方法结果一致。
- 首次应用自动微分和迁移学习于声学问题，加速训练并提升泛化能力。
本文推导了在非均匀介质中一维管道内声波传播的控制方程，将问题转化为无约束优化问题，利用神经网络求解。同时预测声压与质点速度，并与传统的龙格-库塔求解器结果进行验证。研究了温度梯度对声场的影响。展示了自动微分与迁移学习等机器学习技术在声学领域的应用潜力，显著提升计算效率与模型泛化能力。
原文摘要 · Abstract (English)
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.
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