报告承办单位 : pg电子官网入口平台

报告题目 : An  introduction to stochastic inverse problems for  wave equations

（中国彩吧论坛首页字谜总汇大全中国彩吧论坛首页字谜总汇大全中国彩吧论坛首页字谜总汇大全中国彩吧论坛首页字谜总汇大全题中国彩吧论坛首页字谜总汇大全）

报告人姓名 : 中国彩吧论坛首页字谜总汇大全

报告人所在单位 : 中国科学院数学与科学研究院

报告人职称 / 职务及学术头衔 : 副研究员

报告时间 :

2021 年 11 月 22 日（星期一）上午 9 : 3 0-1 1 : 0 0

2021 年 1 1 月 2 4 日（星期三）上午 9 : 3 0-1 1 : 0 0

2021 年 1 1 月 2 6 日（星期五）上午 9 : 3 0-1 1 : 0 0

2021 年 1 1 月 2 9 日（星期一）上午 9 : 3 0-1 1 : 0 0

2021 年 1 2 月 1 日（星期三）上午 9 : 3 0-1 1 : 0 0

报告 方式 : 腾讯会议 ID: 304 1257 8705

报告人中国彩吧论坛首页字谜总汇大全 : 中国彩吧论坛首页字谜总汇大全，20 13 年6月获得厦门大学理学学士学位，后保研至中科院数学与系统科学学院进行硕博连读，并于20 18 年6月获得计算数学博士学位。2 018-2021 年赴美国Purdue University担任Golomb访问助理教授，于2 021 年8月入职中科院数学与系统科学研究院。主要从事中国彩吧论坛首页字谜总汇大全中国彩吧论坛首页字谜总汇大全中国彩吧论坛首页字谜总汇大全范围、中国彩吧论坛首页字谜总汇大全偏微分中国彩吧论坛首页字谜总汇大全数值计算等方面的研究工作，合著有一本学术专著《Lecture Notes in Mathematics  2251 》，并于Springer出版社出版，在 《SIAM 系列》、《Inverse Problems》、《J ournal of Differential Equations 》等期刊发表 SCI 论文数篇.

报告摘要： The inverse problem for wave equations, as an important research subject in the inverse scattering theory, has significant applications in diverse scientific and industrial areas such as antenna design and synthesis, medical imaging, and optical tomography. The stochastic inverse problem refers to the inverse problem that involves uncertainties. Compared to the deterministic counterpart, the stochastic inverse problem is substantially more challenging due to the additional difficulties of randomness and uncertainties.

In th ese  lectures, an introduction to the theory of stochastic analysis will be given first, including Brownian motions, fractional Brownian motions, stochastic integrals, etc. Then a new model for the random source/potential will be presented, which is assumed to be a microlocally isotropic Gaussian random field such that its covariance operator is a classical pseudo-differential operator. Given the random source/potential, the direct problem is to determine the wave field; the inverse problem is to recover the unknown source/potential that generates the prescribed radiated wave field. The well-posedness and regularity of the solution will be addressed for the direct problem.  For the inverse problem, some recent progress on inverse random source/potential problems for the stochastic acoustic, elastic and electromagnetic wave equations will be discussed. Finally, some ongoing and future projects in inverse random potential and medium problems for wave equations will also be highlighted.