
Approximation Properties of Deep ReLU CNNs
This paper is devoted to establishing L^2 approximation properties for d...
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Integral boundary conditions in phase field models
Modeling the microstructure evolution of a material embedded in a device...
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An efficient greedy training algorithm for neural networks and applications in PDEs
Recently, neural networks have been widely applied for solving partial d...
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Characterization of the Variation Spaces Corresponding to Shallow Neural Networks
We consider the variation space corresponding to a dictionary of functio...
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Improved Convergence Rates for the Orthogonal Greedy Algorithm
We analyze the orthogonal greedy algorithm when applied to dictionaries ...
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Sharp Lower Bounds on the Approximation Rate of Shallow Neural Networks
We consider the approximation rates of shallow neural networks with resp...
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ReLU Deep Neural Networks from the Hierarchical Basis Perspective
We study ReLU deep neural networks (DNNs) by investigating their connect...
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Rademacher Complexity and Numerical Quadrature Analysis of Stable Neural Networks with Applications to Numerical PDEs
Methods for solving PDEs using neural networks have recently become a ve...
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Robust BPX preconditioner for the integral fractional Laplacian on bounded domains
We propose and analyze a robust BPX preconditioner for the integral frac...
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Optimal Approximation Rates and Metric Entropy of ReLU^k and Cosine Networks
This article addresses several fundamental issues associated with the ap...
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An Extended Galerkin analysis in finite element exterior calculus
For the Hodge–Laplace equation in finite element exterior calculus, we i...
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HighOrder Approximation Rates for Neural Networks with ReLU^k Activation Functions
We study the approximation properties of shallow neural networks (NN) wi...
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MetaMgNet: Meta Multigrid Networks for Solving Parameterized Partial Differential Equations
This paper studies numerical solutions for parameterized partial differe...
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The Finite Neuron Method and Convergence Analysis
We study a family of H^mconforming piecewise polynomials based on artif...
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Training Sparse Neural Networks using Compressed Sensing
Pruning the weights of neural networks is an effective and widelyused t...
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Helicityconservative finite element discretization for MHD systems
We construct finite element methods for the magnetohydrodynamics (MHD) s...
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An Abstract Stabilization Method with Applications to Nonlinear Incompressible Elasticity
In this paper, we propose and analyze an abstract stabilized mixed finit...
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An Extended Galerkin Analysis for Linear Elasticity with Strongly Symmetric Stress Tensor
This paper presents an extended Galerkin analysis for various Galerkin m...
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Robust block preconditioners for poroelasticity
In this paper we study the linear systems arising from discretized poroe...
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Constrained Linear Datafeature Mapping for Image Classification
In this paper, we propose a constrained linear datafeature mapping mode...
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A machine learning method correlating pulse pressure wave data with pregnancy
Pulse feeling, representing the tactile arterial palpation of the heartb...
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Extended Galerkin Method
A general framework, known as extended Galerkin method, is presented in ...
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On the Approximation Properties of Neural Networks
We prove two new results concerning the approximation properties of neur...
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MgNet: A Unified Framework of Multigrid and Convolutional Neural Network
We develop a unified model, known as MgNet, that simultaneously recovers...
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Modified Regularized Dual Averaging Method for Training Sparse Convolutional Neural Networks
We proposed a modified regularized dual averaging method for training sp...
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Jinchao Xu
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