21 citations · 55 across the 13 of their papers we have counts for
13 papers
Deep Operator Learning Lessens the Curse of Dimensionality for PDEs
Ke Chen, Chunmei Wang, Haizhao Yang
Deep neural networks (DNNs) have achieved remarkable success in numerous domains, and their application to PDE-related problems has been rapidly advancing. This paper provides an e…
Global well-posedness of the 1d compressible Navier-Stokes system with rough data
Ke Chen, Ly Kim Ha, Ruilin Hu +1
In this paper, we study the global well-posedness problem for the 1d compressible Navier-Stokers system (cNSE) in gas dynamics with rough initial data. Frist, Liu- Yu (2022) establ…
Low-rank approximation for multiscale PDEs
Ke Chen, Shi Chen, Qin Li +2
Historically, analysis for multiscale PDEs is largely unified while numerical schemes tend to be equation-specific. In this paper, we propose a unified framework for computing mult…
Global Calderón--Zygmund theory for parabolic -Laplacian system: the case
Ke Chen, Quoc-Hung Nguyen, Na Zhao
The aim of this paper is to establish global Calderón--Zygmund theory to parabolic -Laplacian system: $$ u_t -\operatorname{div}(|\nabla u|^{p-2}\nabla u) = \operatorname{div} (…
The Peskin problem with initial data
Ke Chen, Quoc-Hung Nguyen
In this paper we study the Peskin problem in 2D, which describes the dynamics of a 1D closed elastic structure immersed in a steady Stokes flow. We prove the local well-posedness f…
The Muskat problem with data
Ke Chen, Quoc-Hung Nguyen, Yiran Xu
In this paper we prove that the Cauchy problem of the Muskat equation is wellposed locally in time for any initial data in .
A low-rank Schwarz method for radiative transport equation with heterogeneous scattering coefficient
Ke Chen, Qin Li, Jianfeng Lu +1
Random sampling has been used to find low-rank structure and to build fast direct solvers for multiscale partial differential equations of various types. In this work, we design an…
Random Sampling and Efficient Algorithms for Multiscale PDEs
Ke Chen, Qin Li, Jianfeng Lu +1
We describe a numerical framework that uses random sampling to efficiently capture low-rank local solution spaces of multiscale PDE problems arising in domain decomposition. In con…
Multigrid Algorithm Based on Hybrid Smoothers for Variational and Selective Segmentation Models
Michael Roberts, Ke Chen, Klaus L. Irion
Automatic segmentation of an image to identify all meaningful parts is one of the most challenging as well as useful tasks in a number of application areas. This is widely studied.…
Randomized sampling for basis functions construction in generalized finite element methods
Ke Chen, Qin Li, Jianfeng Lu +1
In the framework of generalized finite element methods for elliptic equations with rough coefficients, efficiency and accuracy of the numerical method depend critically on the use…
Online learning in optical tomography: a stochastic approach
Ke Chen, Qin Li, Jian-Guo Liu
We study the inverse problem of radiative transfer equation (RTE) using stochastic gradient descent method (SGD) in this paper. Mathematically, optical tomography amounts to recove…
Stability of inverse transport equation in diffusion scaling and Fokker-Planck limit
Ke Chen, Qin Li, Li Wang
We consider the inverse problem of reconstructing the scattering and absorption coefficients using boundary measurements for a time dependent radiative transfer equation (RTE). As…
Stability of Stationary Inverse Transport Equation in Diffusion Scaling
Ke Chen, Qin Li, Li Wang
We consider the inverse problem of reconstructing the optical parameters for stationary radiative transfer equation (RTE) from velocity-averaged measurement. The RTE often contains…