Abstract

 In this talk, we discuss three kinds of random Helmholtz problems. For the random interface grating problems, by using the asymptotic perturbation approach via shape derivative, we estimate the expectation and the variance of the random solution in terms of the magnitude of the perturbation. For the optimal control problems constrained by random Helmholtz equation, we preprocess certain quantities before the ADMM iteration, so that nearly no random variable is in the inner iteration. For the inverse scattering problem, we propose a machine learning method for the data retrieval, which can effectively cope with the reconstruction under limited-aperture and/or phaseless far-field data. Numerical experiments verify the promising features of our schemes.

Short bio

张凯教授2006年获吉林大学博士学位，2008年获得香港中文大学联合培养博士学位。2008-2010年，赴密歇根州立大学开展博士后研究。张凯教授先后赴伊利诺伊州立大学，奥本大学，香港浸会大学，南方科技大学等开展合作研究，研究兴趣为随机偏微分方程的数值解法。主要从事随机麦克斯韦方程和随机声波方程控制优化问题，期权定价和套利的数值方法研究。先后主持国家自然科学基金等项目11项，发表论文50余篇，其中SCI论文40余篇。