报告承办单位: 数学与统计学院

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

（随机波动方程反问题简介）

报告人姓名: 王旭

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9:30-11:00

2021年11月24日（星期三）上午9:30-11:00

2021年11月26日（星期五）上午9:30-11:00

2021年11月29日（星期一）上午9:30-11:00

2021年12月1日（星期三）上午9:30-11:00

报告方式: 腾讯会议ID: 304 1257 8705

报告人简介: 王旭，2013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2018年6月获得计算数学博士学位。2018-2021年赴美国Purdue University担任Golomb访问助理教授，于2021年8月入职中科院数学与系统科学研究院。主要从事随机波动方程范围、随机偏微分方程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》、《Journal 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 these 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.