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Computational & Applied Math Seminar

A data-driven and model-based accelerated Hamiltonian Monte Carlo method for Bayesian elliptic inverse problems

  • 演讲者:张智文(香港大学)

  • 时间:2021-10-21 14:00-15:00

  • 地点:腾讯会议 ID 820 421 627

讲座摘要

We propose a data-driven and model-based approach to accelerate the Hamiltonian Monte Carlo (HMC) method in solving large-scale Bayesian inverse problems. The key idea is to exploit (model-based) and construct (data-based) the intrinsic approximate low-dimensional structure of the underlying problem which consists of two components -- a training component that computes a set of data-driven basis to achieve significant dimension reduction in the solution space, and a fast-solving component that computes the solution and its derivatives for a newly sampled elliptic PDE with the constructed data-driven basis. Hence, we achieve an effective data and model-based approach for the Bayesian inverse problem and overcome the typical computational bottleneck of HMC -- repeated evaluation of the Hamiltonian involving the solution (and its derivatives) modeled by a complex system, a multiscale elliptic PDE in our case. We present numerical examples to demonstrate the accuracy and efficiency of the proposed method.   


个人简介
Z. Zhang received his B.S. degree and Ph.D. degree in mathematics from Tsinghua University, Beijing, P.R. China, in 2006 and 2011, respectively. After his graduation, he was a postdoctoral scholar at the California Institute of Technology from 2011 to 2015. He joined the University of Hong Kong as an assistant professor in 2015 and became an associate professor in 2021. Dr. Zhang’s research interests are scientific computation. Research topics include uncertainty quantification, model reduction for parametric partial differential equations (PDEs), nonlinear filtering, stochastic fluid dynamics, and deep learning methods for PDEs.