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

ON2022-04-07TAG: ShanghaiTech UniversityCATEGORY: Lecture

Speaker:    Zhiwen ZhangUniversity of Hong Kong
Time:         15:00-16:00 , Apr.08
Location:   Tencent Meeting
    Meeting ID:649-318-153
Host:          Qifeng Liao&Shixiao Jiang
The speaker will 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, they 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. They present numerical examples to demonstrate the accuracy and efficiency of the proposed method.  
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.