报告题目：Neural-Dynamic Methods for Solving Time-Varying

Tensor Problems

报 告 人：莫长鑫 博士

报告地点：腾讯会议779867515

报告时间：2022年5月13日星期五 19:30-21:00

报告摘要：This presentation mainly covers the neural-dynamic methods for solving time-varying tensor problems. Three time-varying problems are studied. They are the tensor generalized eigenpairs, the multi-linear systems, and the tensor square root problems, which could also be regarded as the generalization of ordinary problems that do not involve any parameters. We present many different types of neural network methods, especially Zhang neural network (ZNN) and gradient-based neural network (GNN), that can be readily adapted to suit the computing of these time-varying problems individually, to compute the time-varying problems we considered.

For the time-varying tensor generalized eigenpairs problem, two different models, the ZNN and varying-parameter ZNN models are proposed. For the time-varying multi-linear systems, two complex-valued neural network models called ZNN model and WsbpPTZNN model are given. We show the WsbpPYZNN model converges to the theoretical solution of the system in predefined-time. For the time-varying tensor square root problem, a new general varying-parameters finite-time convergent Zhang neural network model (VPsFTZNN for short) is proposed. For illustration purposes, various numerical examples, from which we can see that the results are in accordance with the theoretical analysis, are presented. The comparison results with various models further illustrate the reliability and superiority of specific neural-dynamic methods.

报告人简介：莫长鑫，博士，重庆师范大学数学科学学院讲师。2016年6月在中山大学获理学学士学位，2021年6月在复旦大学获理学博士学位。主要研究方向为张量分析、循环神经网络等，在Neurocomputing，Numerical Algorithms，Numer. Math. Theor. Meth. Appl.，Appl. Math. Comput.等国际学术期刊发表学术论文多篇。