报告人:王飞(西安交通大学)
报告题目:Adaptive Growing Randomized Neural Networks for Solving Partial Differential Equations
报告摘要:Traditional numerical methods face numerous challenges in handling high-dimensional problems, complex regional segmentation, and error accumulation caused by time iteration. Concurrently, neural network methods based on optimization training suffer from insufficient accuracy, slow training speeds, and uncontrollable errors due to the lack of efficient optimization algorithms. To combine the advantages of these two approaches and overcome their shortcomings, randomized neural network methods have been proposed. This method not only leverages the strong approximation capabilities of neural networks to circumvent the limitations of classical numerical methods but also aims to resolve issues related to accuracy and training efficiency in neural networks. By incorporating a posterior error estimation as feedback, in this talk, we propose Adaptive Growing Randomized Neural Networks for solving PDEs. This approach can adaptively generate network structures, significantly improving the approximation capabilities.
报告时间:2024年11月8日(星期五)9:30-12:00
报告地点:科技楼南706室
邀请人:柴振华
报告人简介:王飞,西安交通大学数学与统计学院教授、博士生导师,Commun. Nonlinear Sci. Numer. Simul. 副主编。2010年获浙江大学数学博士学位。2010年-2012年,在华中科技大学任教;2012年-2013年,为美国爱荷华大学客座助理教授;2013年-2016年,为美国宾州州立大学Research Associate;2015年入选西安交通大学青年拔尖人才B类(副教授),2017年入选陕西省青年百人,2022年入选西安交通大学青年拔尖人才A类(教授)。研究领域为数值分析与科学计算,主要研究兴趣包括:有限元分析及其应用,变分不等式的数值方法,求解偏微分方程的神经网络方法等。主持国家自然科学基金重大研究计划(培育项目)1项、面上项目2项、青年基金1项。已在国际 SCI 期刊发表论文五十多篇,其中包括计算数学方向的顶级期刊:SIAM J Numer. Anal.,IMA J Numer. Anal.,Numer. Math.,Comput. Methods Appl. Mech. Eng. 等。