GRU稳定性研究及在声波反散射中的应用  

Stability of GRU and its Application in Inverse Scattering Problem of Acoustic Waves

作　　者：王欣羽 孟品超[1] 尹伟石[1] WANG Xinyu;MENG Pinchao;YIN Weishi(School of Mathematics and Statistics,Changchun University of Science and Technology,Changchun 130022)

机构地区：[1]长春理工大学数学与统计学院,长春130022

出　　处：《长春理工大学学报（自然科学版）》2023年第2期136-143,共8页Journal of Changchun University of Science and Technology(Natural Science Edition)

基　　金：吉林省自然科学基金(JJKH20210797KJ)。

摘　　要：针对门控循环单元网络(GRU)的理论研究问题,考虑将GRU与微分方程建立联系,从微分方程的稳定性理论推导神经网络的稳定性。首先,通过GRU网络结构得到网络的动力系统表达形式,用连续方程的前向Euler离散格式解释门控循环单元网络的传播过程。其次,基于Krasovskii方法框架证明离散格式的稳定性,说明单层无输入GRU的稳定性只依赖于候选激活状态下的权重矩阵,并证明GRU的稳定性定理。最后,将GRU应用于求解声波障碍反散射问题,从数值实验角度说明该网络在求解不适定问题时仍能得到稳定的反演效果。Aiming at the theoretical research problem of Gated Recurrent Unit Network(GRU),consider the connection between GRU and differential equations,and derive the stability of neural networks from the stability theory of differential equations.First,obtain the dynamic system expression form of the network through the GRU network structure,and use the forward Euler discrete format of the continuous equation to explain the propagation process of the gated recurrent unit network;Secondly,based on the Krasovskii method framework,the stability of the discrete format is proved,indicating that the stability of a single-layer GRU without input depends only on the weight matrix in the candidate activation state,and the stability theorem of GRU is proved.Finally,GRU is applied to solve the backscattering problem of acoustic obstacles.From the perspective of numerical experiments,it shows that the network can still obtain stable inversion results when solving ill-posed problems.

关 键 词：动力系统 稳定性 门控循环单元网络 反散射问题 

分 类 号：O242.1[理学—计算数学]