报告题目：A data-driven model reduction method for parabolic inverse source problems

报 告 人：张文龙

报告时间：2024年5月24日10:00-11:00

报告地点：格物楼数学研究中心528报告厅

报告摘要：In this talk, we propose a data-driven model reduction method to solve parabolic inverse source problems with uncertain data efficiently. Our method consists of offline and online stages. In the off-line stage, we explore the low-dimensional structures in the solution space of parabolic partial differential equations (PDEs) in the forward problem with a given class of source functions and construct a small number of proper orthogonal decomposition (POD) basis functions to achieve significant dimension reduction. Equipped with the POD basis functions, we can solve the forward problem extremely fast in the online stage. Under a weak regularity assumption on the solution of the parabolic PDEs, we prove the convergence of the POD algorithm in solving the forward parabolic PDEs.

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。