报告题目： Traceability of Water Pollution: An Inversion Scheme via Dynamic CGO Solutions
报 告 人：邱凌云研究员 清华大学
报告时间：2023年4月24日 14:00-15:00
报告地点：腾讯会议 ID：526-653-762
会议链接：https://meeting.tencent.com/dm/IFplsgAoVIZ1
校内联系人：刁怀安 diao@jlu.edu.cn
报告摘要：We aim to find the time-dependent source term in the diffusion equation from the boundary measurement, which allows for the possibility of tracing back the source of pollutants in the environment. Based on the idea of dynamic complex geometrical optics (CGO) solutions, we analyze a variational formulation of the inverse source problem and prove the uniqueness and stability result. A two-step reconstruction algorithm is proposed, which first recovers the locations of the point sources, and then the Fourier components of the emission concentration functions are reconstructed. Numerical experiments on simulated data are conducted. The results demonstrate that our proposed two-step reconstruction algorithm can reliably reconstruct multiple point sources and accurately reconstruct the emission concentration functions. In addition, we decompose the algorithm into two parts: online and offline computation, with most of the work done offline. This paves the way towards real-time traceability of pollution. The proposed method can be used in many fields, particularly those related to water pollution, to identify the source of a contaminant in the environment and can be a valuable tool in protecting the environment.
报告人简介：邱凌云，现任清华大学丘成桐数学科学中心特别研究员、博导，于2013年在美国普渡大学数学系获得博士学位。在加入清华大学之前，其曾在2015年至2018年就职于PGS (Petroleum Geo-Services)位于美国休斯敦的全球研发总部，从事地震波反演问题的研究工作。2013年至2015年，邱凌云博士在明尼苏达大学的IMA(Institute for Mathematics and its Applications)和埃克森美孚位于美国新泽西州的研究与工程中心(ExxonMobil’s Research and Engineering Technology Center)担任联合职位博士后。邱博士的主要研究兴趣包括非线性反问题的分析与计算、最优输运理论、正则化方法、最优化问题的迭代算法以及深度学习在反问题上的应用。
