2 citations · 2 across the 9 of their papers we have counts for
9 papers
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…
Sharp Broken-Power Lorentz Estimates for Fractional Powers of Radial Schrödinger Operators with Inverse-Square Asymptotics
Haochen Liu, Qinghao Yu, Hongyan Zhou
Let be a nonnegative radial Schrödinger operator on , , whose positive harmonic function satisfies for and $U(r…
Sharp and Endpoint Two-Weight Fractional Integral Estimates for Schr"odinger Operators with Inverse-Square Potentials
Haochen Liu, Qinghao Yu, Hongyan Zhou
Let be the Friedrichs extension on , where and lies in the attractive Hardy range. Starting from the known positi…
A High-Order Nyström Method for Coupled Boundary Integral Equations in Oblique-Incidence Scattering by Impedance Cylinders
Haochen Liu, Qinghao Yu
We study the numerical solution of electromagnetic scattering by an infinitely long impedance cylinder under oblique incidence. After separation of the axial phase factor, the axia…
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 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…
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…
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 Partial Differential Equations Using Tensor Neural Network and A Posteriori Error Estimators
Yifan Wang, Zhongshuo Lin, Yangfei Liao +2
In this paper, based on the combination of tensor neural network and a posteriori error estimator, a novel type of machine learning method is proposed to solve high-dimensional bou…