学术空间

Generalization of DeepONets for Learning Operators Arising from a Class of Singularly Perturbed Problems

数学与统计及交叉学科前沿论坛------高端学术讲座第121

报告题目:Generalization of DeepONets for Learning Operators Arising from a Class of Singularly Perturbed Problems

报告人:清华大学黄忠亿教授

时间:73日上午10:30-11:30

地点:阜成路西区综合楼1116会议室


报告内容: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 onedimensional 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.


报告人简介: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,在多尺度数学物理问题的建模、分析和数值模拟等方面取得了一系列创新性成果。2020年获国家杰出青年基金资助,2013年获优秀青年基金资助。