31 citations · 169 across the 22 of their papers we have counts for
16 papers · 1 filter
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…
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 discretization-invariant extension and analysis of some deep operator networks
Zecheng Zhang, Wing Tat Leung, Hayden Schaeffer
We present a generalized version of the discretization-invariant neural operator and prove that the network is a universal approximation in the operator sense. Moreover, by incorpo…
Fast Replica Exchange Stochastic Gradient Langevin Dynamics
Guanxun Li, Guang Lin, Zecheng Zhang +1
Application of the replica exchange (i.e., parallel tempering) technique to Langevin Monte Carlo algorithms, especially stochastic gradient Langevin dynamics (SGLD), has scored gre…
BelNet: Basis enhanced learning, a mesh-free neural operator
Zecheng Zhang, Wing Tat Leung, Hayden Schaeffer
Operator learning trains a neural network to map functions to functions. An ideal operator learning framework should be mesh-free in the sense that the training does not require a…
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…
Hybrid explicit-implicit learning for multiscale problems with time dependent source
Yalchin Efendiev, Wing Tat Leung, Wenyuan Li +1
The splitting method is a powerful method for solving partial differential equations. Various splitting methods have been designed to separate different physics, nonlinearities, an…
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…
HEI: hybrid explicit-implicit learning for multiscale problems
Yalchin Efendiev, Wing Tat Leung, Guang Lin +1
Splitting is a method to handle application problems by splitting physics, scales, domain, and so on. Many splitting algorithms have been designed for efficient temporal discretiza…
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…
Computational multiscale methods for parabolic wave approximations in heterogeneous media
Eric Chung, Yalchin Efendiev, Sai-Mang Pun +1
In this paper, we develop a computational multiscale to solve the parabolic wave approximation with heterogeneous and variable media. Parabolic wave approximation is a technique to…
A deep neural network approach on solving the linear transport model under diffusive scaling
Liu Liu, Tieyong Zeng, Zecheng Zhang
In this work, we propose a learning method for solving the linear transport equation under the diffusive scaling. Due to the multiscale nature of our model equation, the model is c…
A multi-stage deep learning based algorithm for multiscale modelreduction
Eric Chung, Wing Tat Leung, Sai-Mang Pun +1
In this work, we propose a multi-stage training strategy for the development of deep learning algorithms applied to problems with multiscale features. Each stage of the pro-posed s…
Computational multiscale methods for quasi-gas dynamic equations
Boris Chetverushkin, Eric Chung, Yalchin Efendiev +2
In this paper, we consider the quasi-gas-dynamic (QGD) model in a multiscale environment. The model equations can be regarded as a hyperbolic regularization and are derived from ki…
Learning Algorithms for Coarsening Uncertainty Space and Applications to Multiscale Simulations
Zecheng Zhang, Eric Chung, Yalchin Efendiev +1
In this paper, we investigate and design multiscale simulations for stochastic multiscale PDEs. As for the space, we consider a coarse grid and a known multiscale method, the Gener…