12 papers
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…
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…
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…
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…
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…