Convergence analysis of the Multi-scale Deep Neural Network (MscaleDNN)

In this talk, we will present a numerical analysis for the convergence of the machine learning algorithm with Multi-scale neural network. We prove that the training process for some one layer neural networks with gradient descent optimization algorithm tends to diffusion process in the Fourier spectral domain as the learning rate goes to zero. Consequently, the multi-scale neural network is shown to have diffusion coefficients covering a wider range of frequency compared to fully connected neural network.

个人介绍： 
       汪波，湖南师范大学数学与统计学院教授，国家高层次青年人才计划入选者。2011年在湖南师范大学获计算数学博士学位。2011年至2013年在新加坡国立大学从事博士后研究工作。主要研究方向包括超材料中电磁场计算的DG方法、波散射问题高精度方法、界面问题HDG方法、多层媒质中的快速多极法等。在《SIAM J. Sci. Comp.》、《SIAM J. Numer. Anal.》、《Comput. Methods Appl. Mech. Engrg.》、《SIAM J. Appl. Math.》等国内外著名刊物发表论文20多篇，主持国家基金4项。