Speaker: 焦雨领 (武汉大学)

Date: Jan. 16, 2024 (Tuesday)

Beijing Time: 10:00 am-12:00 am

Venue: 恩明楼813 Tencent: 639-783-215

Abstract:

In this presentation, we introduce a deep learning method for parameter identification in elliptic equations. We begin by establishing novel stability estimates that serve as the guiding principle for proposing appropriate loss functions. We propose a model that leverage Tikhonov regularization and physics-informed neural networks (PINNs). Furthermore, we conduct a rigorous analysis for convergence rates of reconstructions which provide valuable a priori insights for the choice of regularization parameters, as well as the size of the neural networks. Finally, we demonstrate the remarkable stability of the method with respect to the data noise through various numerical experiments.

Biography:

焦雨领，武汉大学数学统计学院副教授、博导，入选国家高层次人才青年学者计划。主要从事机器学习、科学计算的研究。现任ACM Transaction on Probabilistic Machine Learning 编委，中国现场统计学会机器学习分会副理事长。相关工作发表在包括Ann. Stat.、J. Amer. Statist. Assoc.、Statist. Sci.、SIAM J. Math. Anal.、SIAM J. Control Optim.、SIAM J. Numer. Anal.、SIAM J. Sci. Comput.、Appl. Comput. Harmon. Anal.、Inverse Probl.、IEEE Trans. Inf. Theory、IEEE Trans. Signal Process.、J. Mach. Learn. Res.、ICML、NeurIPS、AAAI等期刊和会议上。