155 citations · 987 across the 104 of their papers we have counts for
9 papers · 1 filter
High-Order Approximation Rates for Shallow Neural Networks with Cosine and ReLU Activation Functions
Jonathan W. Siegel, Jinchao Xu
We study the approximation properties of shallow neural networks with an activation function which is a power of the rectified linear unit. Specifically, we consider the dependence…
Meta-MgNet: Meta Multigrid Networks for Solving Parameterized Partial Differential Equations
Yuyan Chen, Bin Dong, Jinchao Xu
This paper studies numerical solutions for parameterized partial differential equations (P-PDEs) with deep learning (DL). P-PDEs arise in many important application areas and the c…
The Finite Neuron Method and Convergence Analysis
Jinchao Xu
We study a family of -conforming piecewise polynomials based on artificial neural network, named as the finite neuron method (FNM), for numerical solution of -th order par…
Extensible Structure-Informed Prediction of Formation Energy with Improved Accuracy and Usability employing Neural Networks
Adam M. Krajewski, Jonathan W. Siegel, Jinchao Xu +1
In the present paper, we introduce a new neural network-based tool for the prediction of formation energies of atomic structures based on elemental and structural features of Voron…
Training Sparse Neural Networks using Compressed Sensing
Jonathan W. Siegel, Jianhong Chen, Pengchuan Zhang +1
Pruning the weights of neural networks is an effective and widely-used technique for reducing model size and inference complexity. We develop and test a novel method based on compr…
Helicity-conservative finite element discretization for incompressible MHD systems
Kaibo Hu, Young-Ju Lee, Jinchao Xu
We construct finite element methods for the incompressible magnetohydrodynamics (MHD) system that precisely preserve magnetic and cross helicity, the energy law and the magnetic Ga…
An Abstract Stabilization Method with Applications to Nonlinear Incompressible Elasticity
Qingguo Hong, Chunmei Liu, Jinchao Xu
In this paper, we propose and analyze an abstract stabilized mixed finite element framework that can be applied to nonlinear incompressible elasticity problems. In the abstract sta…
New Discontinuous Galerkin Algorithms and Analysis for Linear Elasticity with Symmetric Stress Tensor
Qingguo Hong, Jun Hu, Limin Ma +1
This paper presents a new and unified approach to the derivation and analysis of many existing, as well as new discontinuous Galerkin methods for linear elasticity problems. The an…
Robust block preconditioners for poroelasticity
Shuangshuang Chen, Qingguo Hong, Jinchao Xu +1
In this paper we study the linear systems arising from discretized poroelasticity problems. We formulate one block preconditioner for the two-filed Biot model and several precondit…