主讲人：张凯 吉林大学教授
时间：2024年6月21日9：00
地点：腾讯会议 627 385 192
举办单位：数理学院
主讲人介绍：张凯教授1999年本科毕业于吉林大学数学系，2006年获吉林大学博士学位，博士论文被评为吉林省优秀博士论文，2008年获得香港中文大学联合培养博士学位，2008-2010年在密歇根州立大学开展博士后研究。2020年被评为吉林大学唐敖庆特聘教授。张凯教授先后赴伊利诺伊州立大学，奥本大学等开展合作研究，主要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，机器学习求解反散射问题的研究。先后主持国家自然科学基金等项目11项，接收发表论文60篇。
内容介绍：This presentation investigates the inverse obstacle scattering problem with low-frequency data in an acoustic waveguide. A Bayesian inference scheme, combining the multi-fidelity strategy and surrogate model with guided modes and deep neural network (DNN), is proposed to reconstruct the shape of unknown scattering objects. Firstly, the inverse problem is reformulated as a statistical inference problem using Bayes' formula, which provides statistical characteristics of the posterior distribution and quantification of the uncertainties. The well-posedness of the posterior distribution is proved by using the f-divergence. Subsequently, a Markov chain Monte Carlo (MCMC) algorithm is used to explore the posterior density. We propose a new multi-fidelity surrogate model to speed up the sampling procedure while maintaining high accuracy. Our numerical simulations demonstrate that this method not only yields high-quality reconstructions but also substantially reduces computational costs.