報告人：張凱（吉林大學）

報告題目：Deep neural network for inverse scattering problems

報告摘要：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 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.

報告時間：2024年10月18日（星期五）16:00-18:00

報告地點：科技樓南706室

邀請人：張誠堅

報告人簡介：張凱，吉林大學數學學院教授、博士生導師, 1999年本科畢業于吉林大學數學系，2006年獲吉林大學博士學位，博士論文被評為吉林省優秀博士論文，2008年獲得香港中文大學聯合培養博士學位，2008-2010年赴密歇根州立大學開展博士後研究, 2020年被評為吉林大學唐敖慶特聘教授。張凱教授先後赴伊利諾伊州立大學，香港城市大學等開展合作研究，主要研究興趣為随機偏微分方程的數值解法。主要從事随機麥克斯韋方程和随機聲波方程，機器學習求解反散射問題的研究, 先後主持國家自然科學基金等項目11項，發表論文62篇。