報告題目： Traceability of Water Pollution: An Inversion Scheme via Dynamic CGO Solutions
報 告 人：邱淩雲研究員 清華大學
報告時間：2023年4月24日 14:00-15:00
報告地點：騰訊會議 ID：526-653-762
會議鍊接：https://meeting.tencent.com/dm/IFplsgAoVIZ1
校内聯系人：刁懷安 diao@jlu.edu.cn
報告摘要：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.
報告人簡介：邱淩雲，現任清華大學丘成桐數學科學中心特别研究員、博導，于2013年在美國普渡大學數學系獲得博士學位。在加入清華大學之前，其曾在2015年至2018年就職于PGS (Petroleum Geo-Services)位于美國休斯敦的全球研發總部，從事地震波反演問題的研究工作。2013年至2015年，邱淩雲博士在明尼蘇達大學的IMA(Institute for Mathematics and its Applications)和埃克森美孚位于美國新澤西州的研究與工程中心(ExxonMobil’s Research and Engineering Technology Center)擔任聯合職位博士後。邱博士的主要研究興趣包括非線性反問題的分析與計算、最優輸運理論、正則化方法、最優化問題的疊代算法以及深度學習在反問題上的應用。
