12 citations · 19 across the 6 of their papers we have counts for
4 papers · 1 filter
Bayesian deep operator learning for homogenized to fine-scale maps for multiscale PDE
Zecheng Zhang, Christian Moya, Wing Tat Leung +2
We present a new framework for computing fine-scale solutions of multiscale Partial Differential Equations (PDEs) using operator learning tools. Obtaining fine-scale solutions of m…
A replica exchange preconditioned Crank-Nicolson Langevin dynamic MCMC method for Bayesian inverse problems
Ou Na, Zecheng Zhang, Guang Lin
This paper proposes a replica exchange preconditioned Langevin diffusion discretized by the Crank-Nicolson scheme (repCNLD) to handle high-dimensional and multi-modal distribution…
Multi-element flow-driven spectral chaos (ME-FSC) method for uncertainty quantification of dynamical systems
Hugo Esquivel, Arun Prakash, Guang Lin
The flow-driven spectral chaos (FSC) is a recently developed method for tracking and quantifying uncertainties in the long-time response of stochastic dynamical systems using the s…
Theoretical and numerical studies of inverse source problem for the linear parabolic equation with sparse boundary measurements
Guang Lin, Zecheng Zhang, Zhidong Zhang
We consider the inverse source problem in the parabolic equation, where the unknown source possesses the semi-discrete formulation. Theoretically, we prove that the flux data from…