A new framework to quantify the uncertainty in general inverse problems

讲座时间 Datetime: 2022年9月9日，星期五，15:00-16:00

地点 Venue: 腾讯线上会议：104248911

主持人 Host：张植栋

报告人 Speaker: 张文龙

单位 Affiliation: 南方科技大学

报告摘要 Abstract:

In this work, we investigate the regularized solutions and their finite element solutions to the inverse source problems governed by partial differential equations, and establish the stochastic convergence and optimal finite element convergence rates of these solutions, under point wise measurement data with random noise. The regularization error estimates and the finite element error estimates are derived with explicit dependence on the noise level, regularization parameter, mesh size, and time step size, which can guide practical choices among these key parameters in real applications. The error estimates also suggest an iterative algorithm for determining an optimal regularization parameter. Numerical experiments are presented to demonstrate the effectiveness of the analytical results.