Speaker: Dr. Ying Liang (梁瑛博士）

Time: 12:10-13:10, 1 December 2023 (Friday) (Beijing time)

Venue: A103,Lijiao Building

Tencent Meeting ID: 943-139-435

Abstract

In the field of inverse problems, the estimation of an unknown source term from indirect observations is a fundamental challenge. In various fields, including antenna synthesis, seismology, and medical imaging, inverse source problems play a pivotal role. Stochastic inverse problems emerge when uncertainties within the model need consideration, and the introduction of random sources further amplifies the complexity due to their inherent uncertainties. In this talk, our focus will be on establishing unified stability estimates for inverse random source problems governed by the stochastic acoustic, biharmonic, and elastic wave equations driven by white noise. We'll provide an overview of existing results for estimating stability of the solution in deterministic settings, and our recent findings will be presented for the stochastic case. we will also discuss potential avenues involving stochastic inverse scattering problems for future research.

About Dr. Liang

Ying Liang is a Golomb Visiting Assistant Professor of Mathematics at the Department of Mathematics of Purdue university. She earned her PhD degree in Mathematics from The Chinese University of Hong Kong in 2021, under the supervision of Prof. Jun Zou. Her research area is in computational and applied mathematics. Her current research interests include ill-posed inverse problems, numerical methods for partial differential equations and scientific machine learning.