Deep Neural Networks and Finite Elements
报告专家：何俊材（阿卜杜拉国王科技大学）
报告时间：2024年4月24日 10:30-11:30
报告地点：数学学院东409报告厅
课程介绍：In this talk, I will discuss our new research on the connection between finite element methods and deep neural network (DNN) functions. At the beginning of the talk, we will first showcase some successful applications of neural networks in both physical and data sciences. Then, I will recall our previous studies that any linear finite element functions, regardless of dimension or mesh, can be represented by DNNs with the ReLU activation function. Extending this finding to finite element functions of arbitrary order has been a challenging problem. In this presentation, we will unveil a solution to this open problem. Specifically, we will demonstrate that finite element functions of any order, constructed on arbitrary simplicial meshes in any dimension, can be represented by a type of DNN equipped with appropriately selected activation functions. Additionally, we will illustrate how this capability to express finite element functions can be utilized to determine an approximation rate for such DNNs.s.
专家简介：何俊材，2014年毕业于四川大学数学与应用数学(试验班)，2019年毕业于北京大学数学科学学院计算数学专业。2019-2020在美国宾夕法尼亚洲立大学数学系做博后。2020-2022任美国德克萨斯大学奥斯汀分校(UT Austin)数学系R. H. Bing Instructor。2022至今在阿卜杜拉国王科技大学(KAUST)做研究科学家，主要的研究兴趣是机器学习与微分方程数值解的理论分析与算法设计。
邀请人：谢小平
