4 papers
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…
Analysis of Convergence for the IPA-AC Method
Xiuzhu Yang, Xiaobo Yin
The Improved Partial Area-Analytical Calculation (IPA-AC) method represents a leading meshfree discretization strategy for peridynamic models, distinguished by its rigorous geometr…
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…
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…