Deep neural networks for waves assisted by the Wiener-Hopf method
Deep neural networks for waves assisted by the Wiener-Hopf method
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Wiener-Hopf 方法辅助的波深度神经网络
DOI：
10.1098/rspa.2019.0846
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发表时间：
2020-03-25
影响因子：
3.5
通讯作者：
Huang, Xun
中科院分区：
文献类型：
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作者：
Huang, Xun
在这项工作中，经典的Wiener-Hopf方法被纳入新兴的深度神经网络来研究某些波动问题。基本思想是使用基于第一原理的分析方法来有效地产生大量数据集，这些数据集将监督数据饥渴的深度神经网络的学习，并进一步解释其工作机制。为了演示这种组合研究策略，首先使用深度前馈网络来近似管道声学问题的前向传播模型，该模型可以在航空发动机噪声测试中找到重要的航空应用。其次，开发了一个卷积型U-net来学习波动方程的空间导数，这有助于促进数学物理和工程应用中的计算范式。提出了对U-net体系结构的几个扩展，以进一步施加可能的物理约束。最后，给出了神经网络的实现细节，并与Wiener-Hopf方法的解析解进行了比较，研究了神经网络的性能。总的来说，这里从一个全新的角度使用了Wiener-Hopf方法，这种组合研究策略应该是这项工作的关键成果。
In this work, the classical Wiener-Hopf method is incorporated into the emerging deep neural networks for the study of certain wave problems. The essential idea is to use the first-principle-based analytical method to efficiently produce a large volume of datasets that would supervise the learning of data-hungry deep neural networks, and to further explain the working mechanisms on underneath. To demonstrate such a combinational research strategy, a deep feed-forward network is first used to approximate the forward propagation model of a duct acoustic problem, which can find important aerospace applications in aeroengine noise tests. Next, a convolutional type U-net is developed to learn spatial derivatives in wave equations, which could help to promote computational paradigm in mathematical physics and engineering applications. A couple of extensions of the U-net architecture are proposed to further impose possible physical constraints. Finally, after giving the implementation details, the performance of the neural networks are studied by comparing with analytical solutions from the Wiener-Hopf method. Overall, the Wiener-Hopf method is used here from a totally new perspective and such a combinational research strategy shall represent the key achievement of this work.