Time: 15:00-16:00, July 5
Location: SIST 1A 108
Host: Prof. Qifeng Liao
Abstract:
There are increasing interest in uncertainty quantification for differential equations with uncertain input data. These data can be the initial conditions, boundary conditions, or the parameters in the differential equations. In this talk, we focus on the uncertainty quantification of inverse problem, under the Bayesian framework. The estimation is given by a posterior probability density. For large scale problems, sampling the posterior can be an extremely challenging task. Markov Chain Monte Carlo (MCMC) provides a general way for sampling but it can be computationally expensive. Gaussian type methods, such as the Ensemble Kalman Filter (EnKF), make Gaussian assumptions even for the possible non-Gaussian posterior, which may lead to inaccuracy. The implicit sampling method is used to sample the posterior density, which combines the prior information about the parameter with the noisy data. The numerical experiments show its efficiency and accuracy by comparing it with the MCMC and some Gaussian approximation methods.
Bio:
Xuemin Tu is an associate professor of Department of Mathematics, University of Kansas, USA. Prof. Tu's research interests include scientific computing and numerical analysis. She works on domain decomposition methods which provide scalable algorithms for large scale computation by reducing original large problems into collections of smaller problems, nonlinear multigrid methods which provide a framework for solving nonlinear system to better utilize the modern computer systems, and nonlinear filters with applications in oceanography.
SIST-Seminar 18182
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