SIAM Journal on Applied Mathematics, Volume 80, Issue 6, Page 2560-2585, January 2020.
We study inverse problems consisting of determining medium properties using the responses to probing waves from the machine learning point of view. Based on the analysis of propagation of waves and their nonlinear interactions, we construct a deep convolutional neural network to reconstruct the coefficients of nonlinear wave equations that model the medium properties. Furthermore, for given approximation accuracy, we obtain the depth and number of units of the network and their quantitative dependence on the complexity of the medium.

中文翻译：

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相空间中的卷积神经网络和逆问题

SIAM应用数学杂志，第80卷，第6期，第2560-2585页，2020年1月。
我们研究反问题，包括从机器学习的角度使用对探测波的响应来确定介质属性。在分析波的传播及其非线性相互作用的基础上，我们构建了一个深层卷积神经网络，以重建建模介质特性的非线性波动方程的系数。此外，对于给定的近似精度，我们获得了网络的深度和数量，以及它们对介质复杂性的定量依赖性。