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

主讲人：黄忠亿 教授

单    位：清华大学

时    间：2025年1月3日 15:00

地    点：学院南阶梯教室

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 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.

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重要创新性成果。2020年获国家杰出青年基金资助，2013年获优秀青年基金资助。