Publications [#374518] of Hongkai Zhao

Papers Published

1. Li, S; Zhang, C; Zhang, Z; Zhao, H, A data-driven and model-based accelerated Hamiltonian Monte Carlo method for Bayesian elliptic inverse problems, Statistics and Computing, vol. 33 no. 4 (August, 2023) [doi]
   (last updated on 2026/01/15)

   Abstract:
   In this paper, we consider a Bayesian inverse problem modeled by elliptic partial differential equations (PDEs). Specifically, 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) 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 develop 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. Finally, we present numerical examples to demonstrate the accuracy and efficiency of the proposed method.