美国密歇根理工大学数学系孙继广教授将于近日在我院做五场系列学术讲座。以下是报告信息，欢迎感兴趣的广大师生参加。

讲座时间：2022年7月18-22日，每日上午8:30-10:00

讲座平台：腾讯会议，会议号647-9636-5091，密码202207

讲座题目：Bayesian methods for inverse problems with partial data

讲座摘要：In this series of lectures, we present some Bayesian inverse scheme for inverse problems with partial data, for which the inverse problems are formulated as a statistical model using the Bayes’ formula. Sampling type methods are used to obtain qualitative prior information for the unknowns and the MCMC algorithm is employed to sample the posterior density functions. We study several inverse problems including the inverse scattering problem, the inverse acoustic source problem, and the inverse moving source problem. Finally, we consider inverse problems with non-unique solutions and introduce two new statistical estimators, the local maximum a posterior (LMAP) and local conditional mean (LCM). A simple algorithm based on clustering to compute LMAP and LCM is proposed. The applications are demonstrated by three examples with multiple solutions: an inverse spectral problem, an inverse source problem, and an inverse medium problem.

The main topics are listed below.

1.     Introduction to Bayesian inverse problems.

2.     Extended-sampling-Bayesian method for limited aperture inverse scattering problems

3.     Quality-Bayesian approach to inverse acoustic source problems with partial data.

4.     A deterministic-statistical approach to reconstruct moving sources using sparse partial data.

5.     Local estimators and Bayesian inverse problems with non-unique solutions.

References

[1] J. Kaipio and E. Somersalo, Statistical and Computational Inverse Problems. Springer, New York, 2005.

[2] Z. Li, Z. Deng, J. Sun, Extended-sampling-Bayesian method for limited aperture inverse scattering problems. SIAM J. Imaging Sci.13 (1), 422-444,2020.

[3] Z. Li, Y. Liu, J. Sun, L. Xu, Quality-Bayesian approach to inverse acoustic source problems with partial data. SIAM J. Sci. Comput.43 (2), A1062-A1080, 2021.

[4] Y. Liu, Y. Guo, J. Sun, A deterministic-statistical approach to reconstruct moving sources using sparse partial data. Inverse Problems 37 (6), 065005, 2021.

[5] J Sun, Local estimators and Bayesian inverse problems with non-unique solutions. Appl. Math. Lett.132, 108149, 2022.

主讲人简介：孙继广1996年在清华大学应用数学系获得学士学位，2005年在University of Delaware获得应用数学博士。现在任Michigan Technological University教授。研究方向包括特征值问题有限元方法和逆散射理论：传输特征值的计算，非共轭矩阵特征值的围道积分方法，非线性特征值计算收敛性分析的解析算子函数方法，反散射问题的采样法，贝叶斯反问题以及穿墙探测问题。从2004年至今发表80余篇文章以及一部合作的专著Finite Element Methods for Eigenvalue Problems，Taylor & Francis，2016。