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報告承辦單位: 數學與統計學院

報告題目: An introduction to stochastic inverse problems for wave equations

（隨機波動方程反問題簡介）

報告人姓名: 王旭

報告人所在單位: 中國科學院數學與科學研究院

報告人職稱/職務及學術頭銜: 副研究員

報告時間:

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

報告方式: 騰訊會議ID: 304 1257 8705

報告人簡介: 王旭，2013年6月獲得廈門大學理學學士學位，后保研至中科院數學與系統科學學院進行碩博連讀，并于2018年6月獲得計算數學博士學位。2018-2021年赴美國Purdue University擔任Golomb訪問助理教授，于2021年8月入職中科院數學與系統科學研究院。主要從事隨機波動方程范圍、隨機偏微分方程數值計算等方面的研究工作，合著有一本學術專著《Lecture Notes in Mathematics 2251》，并于Springer出版社出版，在《SIAM 系列》、《Inverse Problems》、《Journal of Differential Equations》等期刊發表SCI論文數篇.

報告摘要：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.