求解t-积下时变张量方程的自适应梯度神经网络模型  

Adaptive Gradient Neural Network Model for Solving Time-Varying Tensor Equations under T-Product

作　　者：代红艳 莫长鑫 DAI Hongyan;MO Changxin(School of Mathematical Science,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《东莞理工学院学报》2025年第1期10-14,共5页Journal of Dongguan University of Technology

基　　金：重庆市自然科学基金面上项目(CSTB2022NSCQ-MSX0896);重庆市教委科学技术研究计划青年项目(KJQN202200512);重庆师范大学校级基金项目(21XLB040)。

摘　　要：从控制角度研究了张量t积下时变张量方程A(t)*X(t)=B(t)的求解模型。利用张量t积性质与矩阵化技巧,并基于Lyapunov理论,提出了一种求解时变张量方程的自适应梯度神经网络模型—T-AGNN模型。理论上证明了T-AGNN模型的收敛性,确保其求解过程的稳定性和可靠性。数值实验进一步验证了模型的可行性,与现有模型比较结果表明:T-AGNN模型在求解效率上具有显著优势,且模型性能可通过参数与激活函数的调整得到进一步提升,展现了模型的有效性。This paper studies the computation model of time-varying tensor equations under the tensor t-product from the perspective of control theory.By utilizing the properties of tensor t-products and matrix transformation techniques,and based on Lyapunov theory,an adaptive gradient neural network model—the T-AGNN model-for solving time-varying tensor equations is proposed.Theoretically,the convergence result of the T-AGNN model is established,ensuring the stability and reliability of its solution process.Numerical experiments with various activation functions are conducted to verify the performance of the model.By comparing the T-AGNN model with other existing models,we find that the T-AGNN model outperforms others and its convergence speed can be further improved by adjusting the parameters and activation functions,which further shows its efficiency.

关 键 词：时变张量方程 张量t积 LYAPUNOV理论 自适应梯度神经网络模型 

分 类 号：O24[理学—计算数学]