35 citations · 146 across the 37 of their papers we have counts for
26 papers · 1 filter
A Hybrid Discontinuous Galerkin Neural Network Method for Solving Hyperbolic Conservation Laws with Temporal Progressive Learning
Yan Shen, Jingrun Chen, Keke Wu
For hyperbolic conservation laws, traditional methods and physics-informed neural networks (PINNs) often encounter difficulties in capturing sharp discontinuities and maintaining t…
Numerical Homogenization of Landau-Lifshitz Equation with Rough Coefficients
Zetao Ma, Jingrun Chen, Rui Du +1
In this work, we develop a numerical homogenization approach for the fully nonlinear Landau-Lifshitz equation with rough coefficients, including non-periodicity and nonseparable sc…
Finite volume element method for Landau-Lifshitz equation
Yunjie Gong, Jingrun Chen, Rui Du +1
The Landau-Lifshitz equation describes the dynamics of magnetization in ferromagnetic materials. Due to the essential nonlinearity and nonconvex constraint, it is typically solved…
A Micro-Macro Decomposition-Based Asymptotic-Preserving Random Feature Method for Multiscale Radiative Transfer Equations
Jingrun Chen, Zheng Ma, Keke Wu
This paper introduces the Asymptotic-Preserving Random Feature Method (APRFM) for the efficient resolution of multiscale radiative transfer equations. The APRFM effectively address…
R-adaptive DeepONet: Learning Solution Operators for PDEs with Discontinuous Solutions Using an R-adaptive Strategy
Yameng Zhu, Jingrun Chen, Weibing Deng
DeepONet has recently been proposed as a representative framework for learning nonlinear mappings between function spaces. However, when it comes to approximating solution operator…
XI-DeepONet: An operator learning method for elliptic interface problems
Ran Bi, Jingrun Chen, Weibing Deng
Scientific computing has been an indispensable tool in applied sciences and engineering, where traditional numerical methods are often employed due to their superior accuracy guara…
IMEX-RK methods for Landau-Lifshitz equation with arbitrary damping
Yan Gui, Cheng Wang, Jingrun Chen
Magnetization dynamics in ferromagnetic materials is modeled by the Landau-Lifshitz (LL) equation, a nonlinear system of partial differential equations. Among the numerical approac…
Solving multiscale elliptic problems by sparse radial basis function neural networks
Zhiwen Wang, Minxin Chen, Jingrun Chen
Machine learning has been successfully applied to various fields of scientific computing in recent years. In this work, we propose a sparse radial basis function neural network met…
The Random Feature Method for Solving Interface Problems
Xurong Chi, Jingrun Chen, Zhouwang Yang
Interface problems have long been a major focus of scientific computing, leading to the development of various numerical methods. Traditional mesh-based methods often employ time-c…
The Random Feature Method for Time-dependent Problems
Jingrun Chen, Weinan E, Yixin Luo
We present a framework for solving time-dependent partial differential equations (PDEs) in the spirit of the random feature method. The numerical solution is constructed using a sp…
Micromagnetics simulations and phase transitions of ferromagnetics with Dzyaloshinskii-Moriya interaction
Panchi Li, Shuting Gu, Jin Lan +3
Magnetic skyrmions widely exist in a diverse range of magnetic systems, including chiral magnets with a non-centrosymmetric structure characterized by Dzyaloshinkii-Moriya interact…
Convergence analysis of an implicit finite difference method for the inertial Landau-Lifshitz-Gilbert equation
Jingrun Chen, Panchi Li, Cheng Wang
The Landau-Lifshitz-Gilbert (LLG) equation is a widely used model for fast magnetization dynamics in ferromagnetic materials. Recently, the inertial LLG equation, which contains an…
Bridging Traditional and Machine Learning-based Algorithms for Solving PDEs: The Random Feature Method
Jingrun Chen, Xurong Chi, Weinan E +1
One of the oldest and most studied subject in scientific computing is algorithms for solving partial differential equations (PDEs). A long list of numerical methods have been propo…
Convergence Analysis of A Second-order Accurate, Linear Numerical Scheme for The Landau-Lifshitz Equation with Large Damping Parameters
Yongyong Cai, Jingrun Chen, Cheng Wang +1
A second order accurate, linear numerical method is analyzed for the Landau-Lifshitz equation with large damping parameters. This equation describes the dynamics of magnetization,…
A second-order semi-implicit method for the inertial Landau-Lifshitz-Gilbert equation
Panchi Li, Lei Yang, Jin Lan +2
Recent theoretical and experimental advances show that the inertia of magnetization emerges at sub-picoseconds and contributes to the ultrafast magnetization dynamics which cannot…
Roughness Index for Loss Landscapes of Neural Network Models of Partial Differential Equations
Keke Wu, Xiangru Jian, Rui Du +2
Loss landscape is a useful tool to characterize and compare neural network models. The main challenge for analysis of loss landscape for the deep neural networks is that they are g…
A Gauss-Seidel projection method with the minimal number of updates for stray field in micromagnetic simulations
Panchi Li, Zetao Ma, Rui Du +1
Magnetization dynamics in magnetic materials is often modeled by the Landau-Lifshitz equation, which is solved numerically in general. In micromagnetic simulations, the computation…
A Machine-Learning Method for Time-Dependent Wave Equations over Unbounded Domains
Changjian Xie, Jingrun Chen, Xiantao Li
Time-dependent wave equations represent an important class of partial differential equations (PDE) for describing wave propagation phenomena, which are often formulated over unboun…
Enforcing exact boundary and initial conditions in the deep mixed residual method
Liyao Lyu, Keke Wu, Rui Du +1
In theory, boundary and initial conditions are important for the wellposedness of partial differential equations (PDEs). Numerically, these conditions can be enforced exactly in cl…
A comparison study of deep Galerkin method and deep Ritz method for elliptic problems with different boundary conditions
Jingrun Chen, Rui Du, Keke Wu
Recent years have witnessed growing interests in solving partial differential equations by deep neural networks, especially in the high-dimensional case. Unlike classical numerical…
Two improved Gauss-Seidel projection methods for Landau-Lifshitz-Gilbert equation
Panchi Li, Changjian Xie, Rui Du +2
In this paper, we present two improved Gauss-Seidel projection methods with unconditional stability. The first method updates the gyromagnetic term and the damping term simultaneou…
A multiscale finite element method for the Schrödinger equation with multiscale potentials
Jingrun Chen, Dingjiong Ma, Zhiwen Zhang
In recent years, an increasing attention has been paid to quantum heterostructures with tailored functionalities, such as heterojunctions and quantum matematerials, in which quantu…
Estimation of exciton diffusion lengths of organic semiconductors in random domains
Jingrun Chen, Ling Lin, Zhiwen Zhang +1
Exciton diffusion length plays a vital role in the function of opto-electronic devices. Oftentimes, the domain occupied by an organic semiconductor is subject to surface measuremen…
Analysis of the divide-and-conquer method for electronic structure calculations
Jingrun Chen, Jianfeng Lu
We study the accuracy of the divide-and-conquer method for electronic structure calculations. The analysis is conducted for a prototypical subdomain problem in the method. We prove…