2 citations · 5 across the 8 of their papers we have counts for
9 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--…
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…
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…
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…
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…
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…
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…
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…