天元名家讲座|Linearized Inverse Schrodinger Potential Problem with Partial Data and Its DNN Inversion
报 告 人: 陆帅 教授
所在单位: 复旦大学
报告地点: 腾讯会议
报告时间: 2022-06-24 14:00:00
报告简介:

腾讯会议:627-744-912

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Inverse Schrodinger potential problem concerns about the recovery of potential function in the Schrodinger equation in bounded domain throught DtN map. In this talk, we introduce the linearized local DtN map in the partial data setting, and prove a stability estimate with explicit dependence on wavenumber. This is an increasing stability result, in the sense that the logarithmic stable term decays when wavenumber increases. Furthermore, a heuristic DNN algorithm based on a regularization scheme is applied and the stability improvement with respect to the wavenumber is observed. It is a joint work with Boxi Xu (SUFE) and Sen Zou (Fudan).

 

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主讲人简介:
陆帅,复旦大学数学科学学院教授,主要从事数学物理反问题计算方法与数学理论的研究,特别是反问题正则化方法收敛性分析及偏微分方程反问题稳定性理论等。至今在Inverse Problems、SIAM系列、Numer. Math.、Math. Comp.等权威期刊共发表学术论文五十余篇,合作出版英文学术专著一本。2019年获得国家杰出青年科学基金资助,现任《Inverse Problems》的编委,曾获上海市自然科学奖一等奖(第二完成人)。