主講人：張凱 吉林大學教授
時間：2024年6月21日9：00
地點：騰訊會議 627 385 192
舉辦單位：數(shù)理學院
主講人介紹：張凱教授1999年本科畢業(yè)于吉林大學數(shù)學系，2006年獲吉林大學博士學位，博士論文被評為吉林省優(yōu)秀博士論文，2008年獲得香港中文大學聯(lián)合培養(yǎng)博士學位，2008-2010年在密歇根州立大學開展博士后研究。2020年被評為吉林大學唐敖慶特聘教授。張凱教授先后赴伊利諾伊州立大學，奧本大學等開展合作研究，主要研究興趣為隨機偏微分方程的數(shù)值解法。主要從事隨機麥克斯韋方程和隨機聲波方程，機器學習求解反散射問題的研究。先后主持國家自然科學基金等項目11項，接收發(fā)表論文60篇。
內(nèi)容介紹：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.