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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…