报告题目：Stochastic convergence of regularized solutions for backward heat conduction problems
报 告 人：张文龙（南方科技大学 副教授）
会议时间：2023/11/16 上午10:00开始
会议地点：腾讯会议，会议号：548-724-077，密码231116
报告摘要：In this talk, we study the stochastic convergence of regularized solutions for backward heat conduction problems. These problems are recognized as ill-posed due to the exponential decay of eigenvalues associated with the forward problems. We derive an error estimate for the least-squares regularized minimization problem within the framework of stochastic convergence. Our analysis reveals that the optimal error of the Tikhonov-type least-squares optimization problem depends on the noise level, the number of sensors, and the underlying ground truth. Moreover, we propose a self-adaptive algorithm to identify the optimal regularization parameter for the optimization problem without requiring knowledge of the noise level or any other prior information, which will be very practical in applications. We present numerical examples to demonstrate the accuracy and efficiency of our proposed method. These numerical results show that our method is efficient in solving backward heat conduction problems.
报告人简介：张文龙，数学博士，本科毕业于南京大学，先后在中国科学院，巴黎高等师范学校获得硕士博士学位，现任南方科技大学助理教授。研究方向包括反问题理论数值计算、不确定性量化、数值分析等。主持国家自然科学基金青年基金和面上基金，主持深圳市博士启动项目，获得深圳市海外高层次人才C类。在Siam系列，Inverse Problems等杂志发表十余篇论文。
