主講人：張凱 吉林大學(xué)教授

時(shí)間：2024年6月21日9：00

地點(diǎn)：騰訊會(huì)議 627 385 192

舉辦單位：數(shù)理學(xué)院

主講人介紹：張凱教授1999年本科畢業(yè)于吉林大學(xué)數(shù)學(xué)系，2006年獲吉林大學(xué)博士學(xué)位，博士論文被評(píng)為吉林省優(yōu)秀博士論文，2008年獲得香港中文大學(xué)聯(lián)合培養(yǎng)博士學(xué)位，2008-2010年在密歇根州立大學(xué)開展博士后研究。2020年被評(píng)為吉林大學(xué)唐敖慶特聘教授。張凱教授先后赴伊利諾伊州立大學(xué)，奧本大學(xué)等開展合作研究，主要研究興趣為隨機(jī)偏微分方程的數(shù)值解法。主要從事隨機(jī)麥克斯韋方程和隨機(jī)聲波方程，機(jī)器學(xué)習(xí)求解反散射問題的研究。先后主持國(guó)家自然科學(xué)基金等項(xiàng)目11項(xiàng)，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.