报告题目：DNN forinverse scattering problems

报告人：张凯教授吉林大学

报告时间：2023年10月20日 10:00-12:30

报告地点：腾讯会议394 751 806

报告摘要：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 provedby 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.

张凯，吉林大学数学院教授，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年赴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，机器学习求解反散色问题的研究，接收发表论文60篇，部分成果发表在SIAM Appl. Math., J. Comput. Phys.,IMA J. Numer. Anal.等应用、计算数学领域著名期刊,先后主持国家自然科学基金等项目11项.