报告题目:DNN for inverse scattering problems
报告时间:2024-10-22 10:00-11:00
报 告 人:张凯 教授(吉林大学)
报告地点:理学院东北楼四楼报告厅(404)
Abstract: 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.
