2 citations · 6 across the 24 of their papers we have counts for
27 papers
Improved leading coefficient in the individual Berezin-Li-Yau bound via energy orthogonality
Yifan Wang, Hehu Xie
Let be the th eigenvalue of the Dirichlet Laplacian on an open set of finite positive measure. The direct individual consequence of the Berezin--Li--…
Toward Pólya's Conjecture: Improving the Individual Li-Yau Bound via Energy Orthogonality
Yifan Wang, Hehu Xie
We establish two complementary lower-bound mechanisms for individual eigenvalues of the Dirichlet Laplacian. First, energy orthogonality yields a frequency-dependent cap on the Fou…
Mini mixed finite element method for nearly incompressible linear elasticity problems
Zhijin Guan, Yue Feng, Hehu Xie +1
This paper addresses the numerical solution of nearly incompressible linear elasticity boundary value problems and their associated eigenvalue problems. A mixed finite element form…
A Tensor Neural Network Method for High-Order Homogenization of Locally Periodic Elliptic Problems
Huaijia Zhang, Haochen Liu, Xia Ji +1
We develop a high-order tensor neural network (TNN) method for locally periodic elliptic multiscale problems of the form . B…
fTNN: a tensor neural network for fractional PDEs
Qingkui Ma, Hehu Xie, Xiaobo Yin
We develop the fTNN, a deterministic tensor neural network subspace method for problems involving the fractional Laplacian on bounded domains, taking the fractional Poisson equatio…
Quadrature-Enhanced Monte Carlo fPINN Method for High-Dimensional Fractional PDEs
Qingkui Ma, Hehu Xie, Xiaobo Yin
Fractional PDEs involving the fractional Laplacian on bounded domains are challenging because of hypersingular nonlocal kernels, exterior Dirichlet constraints, reduced boundary re…
Regularity Analysis and Tensor Neural Network Methods for Quasiperiodic Elliptic Equations
Jingze Ren, Yifan Wang, Hehu Xie +1
This paper investigates quasiperiodic elliptic equations using a well-established projection method, by which the original problem is reformulated as a degenerate periodic variatio…
Spectral convergence of sum-of-Gaussians tensor neural networks for many-electron Schrödinger equation
Teng Wu, Qi Zhou, Huangjie Zheng +2
We present an improved version of the sum-of-Gaussians tensor neural network (SOG-TNN) architecture for solving many-electron Schrödinger equation for one-dimensional soft-Coulomb…
Continuous Finite Element Method For Maxwell Eigenvalue Problems With Regular Decomposition Technique
Feiyi Liao, Haochen Liu, Hehu Xie
With the regular decomposition technique, we decompose the space into the sum of a vector potential space and the gradient of a scalar space, bot…
A Robust GPU-Accelerated Kernel Compensation Solver with Novel Discretization for Photonic Crystals in Anisotropic Media
Chenhao Jin, Hehu Xie
This paper develops a robust solver for the Maxwell eigenproblem in 3D photonic crystals with anisotropic media. The solver employs the kernel compensation technique under the fram…
A finite-element Delta-Sternheimer approach for computing accurate all-electron RPA correlation energies of polyatomic molecules
Hao Peng, Haochen Liu, Chuhao Li +2
Attaining a reliable complete basis set (CBS) limit remains a significant challenge in ab initio correlated electronic-structure calculations. Building on our previous work for ato…
The Weak Galerkin and Crouzeix-Raviart element method for elastic eigenvalue problems
Wei Lu, Hehu Xie, Qilong Zhai
In this paper, we first introduce an abstract framework to solve the eigenvalue problem by weak Galerkin (WG) method. By the application of the framework, WG method is proved to be…
Sum-of-Gaussians tensor neural networks for high-dimensional Schrödinger equation
Qi Zhou, Teng Wu, Jianghao Liu +3
We propose an accurate, efficient, and low-memory sum-of-Gaussians tensor neural network (SOG-TNN) algorithm for solving the high-dimensional Schrödinger equation. The SOG-TNN util…
Neural Network Element Method for Partial Differential Equations
Yifan Wang, Zhongshuo Lin, Hehu Xie
In this paper, based on the combination of finite element mesh and neural network, a novel type of neural network element space and corresponding machine learning method are design…
Solving Time-Fractional Partial Integro-Differential Equations Using Tensor Neural Network
Zhongshuo Lin, Qingkui Ma, Hehu Xie +1
In this paper, we propose a novel machine learning method based on adaptive tensor neural network subspace to solve linear time-fractional diffusion-wave equations and nonlinear ti…
PASE: A Massively Parallel Augmented Subspace Eigensolver for Large Scale Eigenvalue Problems
Yangfei Liao, Haochen Liu, Hehu Xie +1
In this paper, we present a novel parallel augmented subspace method and build a package Parallel Augmented Subspace Eigensolver (PASE) for solving large scale eigenvalue problems…
Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy
Zhongshuo Lin, Yifan Wang, Hehu Xie
Based on neural network and adaptive subspace approximation method, we propose a new machine learning method for solving partial differential equations. The neural network is adopt…
FieldTNN-based machine learning method for Maxwell eigenvalue problems
Jiantao Jiang, Yanli Wang, Yifan Wang +1
The aim of this paper is to introduce a FieldTNN-based machine learning method for solving the Maxwell eigenvalue problem in both 2D and 3D domains, including both tensor and non-t…
Error estimates of finite element methods for nonlocal problems using exact or approximated interaction neighborhoods
Qiang Du, Hehu Xie, Xiaobo Yin +1
We study the asymptotic error between the finite element solutions of nonlocal models with a bounded interaction neighborhood and the exact solution of the limiting local model. Th…
Enhanced Error Estimates for Augmented Subspace Method with Crouzeix-Raviart Element
Zhijin Guan, Yifan Wang, Hehu Xie +1
In this paper, we present some enhanced error estimates for augmented subspace methods with the nonconforming Crouzeix-Raviart (CR) element. Before the novel estimates, we derive t…
A Nonnested Augmented Subspace Method for Kohn-Sham Equation
Guanghui Hu, Hehu Xie, Fei Xu +1
In this paper, a novel adaptive finite element method is proposed to solve the Kohn-Sham equation based on the moving mesh (nonnested mesh) adaptive technique and the augmented sub…
Tensor Neural Network Interpolation and Its Applications
Yongxin Li, Zhongshuo Lin, Yifan Wang +1
Based on tensor neural network, we propose an interpolation method for high dimensional non-tensor-product-type functions. This interpolation scheme is designed by using the tensor…
Tensor Neural Network Based Machine Learning Method for Elliptic Multiscale Problems
Zhongshuo Lin, Haochen Liu, Hehu Xie
In this paper, we introduce a type of tensor neural network based machine learning method to solve elliptic multiscale problems. Based on the special structure, we can do the direc…
Solving High-dimensional Parametric Elliptic Equation Using Tensor Neural Network
Hongtao Chen, Rui Fu, Yifan Wang +1
In this paper, we introduce a tensor neural network based machine learning method for solving the elliptic partial differential equations with random coefficients in a bounded phys…