31 citations · 84 across the 14 of their papers we have counts for
12 papers
Graph Neural Multilevel Preconditioners for Iterative Solvers
Zechen Zhang, Rui Peng Li, Yousef Saad
Solving large, sparse linear systems is a core task in scientific computing, and efficient iterative solvers rely critically on effective and robust preconditioning. While classica…
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…
Accelerated replica exchange stochastic gradient Langevin diffusion enhanced Bayesian DeepONet for solving noisy parametric PDEs
Guang Lin, Christian Moya, Zecheng Zhang
The Deep Operator Networks~(DeepONet) is a fundamentally different class of neural networks that we train to approximate nonlinear operators, including the solution operator of par…
NH-PINN: Neural homogenization based physics-informed neural network for multiscale problems
Wing Tat Leung, Guang Lin, Zecheng Zhang
Physics-informed neural network (PINN) is a data-driven approach to solve equations. It is successful in many applications; however, the accuracy of the PINN is not satisfactory wh…
Multi-variance replica exchange stochastic gradient MCMC for inverse and forward Bayesian physics-informed neural network
Guang Lin, Yating Wang, Zecheng Zhang
Physics-informed neural network (PINN) has been successfully applied in solving a variety of nonlinear non-convex forward and inverse problems. However, the training is challenging…
Graph coarsening: From scientific computing to machine learning
Jie Chen, Yousef Saad, Zechen Zhang
The general method of graph coarsening or graph reduction has been a remarkably useful and ubiquitous tool in scientific computing and it is now just starting to have a similar imp…