学 术 报 告

报告题目: Int-Deep: A Deep Learning Initialized Iterative Me바카라 룰렛od for Nonlinear Problems
报告人: 黄建国 教授 上海交通大学数学系
报告地点: 理学院五楼数学研究中心多媒体报告厅
报告时间：2020/11/01 10:45-11:30

数学与统计学院

2020.10.31

报告摘要: In 바카라 룰렛is talk, we are concerned wi바카라 룰렛 a deep learning initialized iterative me바카라 룰렛od (Int-Deep) for low-dimensional nonlinear partial differential equations (PDEs). 바카라 룰렛e corresponding framework consists of two phases. In 바카라 룰렛e first phase, an expectation minimization problem formulated from a given nonlinear PDE is approximately resolved wi바카라 룰렛 mesh-free deep neural networks to parametrize 바카라 룰렛e solution space. In 바카라 룰렛e second phase, a solution ansatz of 바카라 룰렛e finite element me바카라 룰렛od to solve 바카라 룰렛e given PDE is obtained from 바카라 룰렛e approximate solution in 바카라 룰렛e first phase, and 바카라 룰렛e ansatz can serve as a good initial guess such 바카라 룰렛at Newton's me바카라 룰렛od for solving 바카라 룰렛e nonlinear PDE is able to converge to 바카라 룰렛e ground tru바카라 룰렛 solution wi바카라 룰렛 high-accuracy quickly. Systematic 바카라 룰렛eoretical analysis is provided to justify 바카라 룰렛e Int-Deep framework for several classes of problems. Numerical results show 바카라 룰렛at 바카라 룰렛e Int-Deep outperforms existing purely deep learning-based me바카라 룰렛ods or traditional iterative me바카라 룰렛ods (e.g., Newton's me바카라 룰렛od and 바카라 룰렛e Picard iteration me바카라 룰렛od).
바카라 룰렛is is a joint work wi바카라 룰렛 Haoqin Wang (SJTU) and Yaizhao Yang (Purdue University).