京师数学前沿论坛 第十一讲
京师数学前沿论坛
报告题目(Title)：Generalization of DeepONets for Learning Operators Arising from a Class of Singularly Perturbed Problems
报告人(Speaker)：黄忠亿 教授 （清华大学）
地点(Place)：后主楼1124
时间(Time)：12月25日16:00-17:00
报告摘要
Singularly perturbed problems present inherent difficulty due to the presence of boundary/interior layers in its solution. To overcome this difficulty, we propose using deep operator networks (DeepONets). In this talk, we demonstrate for the first time the application of DeepONets to one dimensional singularly perturbed problems. We consider the convergence rate of the approximation error incurred by the operator networks in approximating the solution operator, and examine the generalization gap and empirical risk, all of which are shown to converge uniformly with respect to the perturbation parameter.
主讲人简介
黄忠亿，清华大学数学科学系长聘教授、博士生导师，一直从事计算数学与科学工程计算方面的研究。2020年获国家杰出青年基金资助，2013年获优秀青年基金资助。
