7 papers
Generalization Error Curves for Analytic Spectral Algorithms under Power-law Decay
Yicheng Li, Weiye Gan, Zuoqiang Shi +1
The generalization error curve of certain kernel regression method aims at determining the exact order of generalization error with various source condition, noise level and choice…
A seamless local-nonlocal coupling diffusion model with vanishing nonlocality convergence
Yanzun Meng, Zuoqiang Shi
Based on the development in dealing with nonlocal boundary conditions, we propose a seamless local-nonlocal coupling diffusion model in this paper. In our model, a finite constant…
Asymptotically Compatible Error Bound of Finite Element Method for Nonlocal Diffusion Model with An Efficient Implementation
Yanzun Meng, Zuoqiang Shi
This paper presents an asymptotically compatible error bound for the finite element method (FEM) applied to a nonlocal diffusion model. The analysis covers two scenarios: meshes wi…
A Nonlocal Biharmonic Model with -Convergence to Local Model and an Efficient Numerical Method
Weiye Gan, Tangjun Wang, Qiang Du +1
Nonlocal models and their associated theories have been extensively investigated in recent years. Among these, nonlocal versions of the classical Laplace operator have attracted th…
Neural Tangent Kernel of Neural Networks with Loss Informed by Differential Operators
Weiye Gan, Yicheng Li, Qian Lin +1
Spectral bias is a significant phenomenon in neural network training and can be explained by neural tangent kernel (NTK) theory. In this work, we develop the NTK theory for deep ne…
-convergence of Nonlocal Dirichlet Energies With Penalty Formulations of Dirichlet Boundary Data
Weiye Gan, Qiang Du, Zuoqiang Shi
We study nonlocal Dirichlet energies associated with a class of nonlocal diffusion models on a bounded domain subject to the conventional local Dirichlet boundary condition. The go…