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09/21/2023
AceGPT, Localizing Large Language Models in Arabic
This paper explores the imperative need and methodology for developing a...
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05/17/2023
DualFL: A Duality-based Federated Learning Algorithm with Communication Acceleration in the General Convex Regime
We propose a novel training algorithm called DualFL (Dualized Federated ...
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02/02/2023
FV-MgNet: Fully Connected V-cycle MgNet for Interpretable Time Series Forecasting
By investigating iterative methods for a constrained linear model, we pr...
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11/22/2022
A neuron-wise subspace correction method for the finite neuron method
In this paper, we propose a novel algorithm called Neuron-wise Parallel ...
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08/09/2022
On the Activation Function Dependence of the Spectral Bias of Neural Networks
Neural networks are universal function approximators which are known to ...
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07/05/2022
A sharp Korn's inequality for piecewise H^1 space and its application
In this paper, we revisit Korn's inequality for the piecewise H^1 space ...
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07/04/2022
An efficient iterative method for dynamical Ginzburg-Landau equations
In this paper, we propose a new finite element approach to simulate the ...
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12/14/2021
An Interpretive Constrained Linear Model for ResNet and MgNet
We propose a constrained linear data-feature-mapping model as an interpr...
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09/01/2021
Approximation Properties of Deep ReLU CNNs
This paper is devoted to establishing L^2 approximation properties for d...
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08/15/2021
Integral boundary conditions in phase field models
Modeling the microstructure evolution of a material embedded in a device...
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07/09/2021
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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06/28/2021
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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06/28/2021
Improved Convergence Rates for the Orthogonal Greedy Algorithm
We analyze the orthogonal greedy algorithm when applied to dictionaries ...
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06/28/2021
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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05/10/2021
ReLU Deep Neural Networks from the Hierarchical Basis Perspective
We study ReLU deep neural networks (DNNs) by investigating their connect...
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04/07/2021
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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03/23/2021
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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01/29/2021
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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01/24/2021
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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12/14/2020
High-Order 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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10/27/2020
Meta-MgNet: Meta Multigrid Networks for Solving Parameterized Partial Differential Equations
This paper studies numerical solutions for parameterized partial differe...
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10/04/2020
The Finite Neuron Method and Convergence Analysis
We study a family of H^m-conforming piecewise polynomials based on artif...
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08/21/2020
Training Sparse Neural Networks using Compressed Sensing
Pruning the weights of neural networks is an effective and widely-used t...
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07/15/2020
Helicity-conservative finite element discretization for MHD systems
We construct finite element methods for the magnetohydrodynamics (MHD) s...
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05/01/2020
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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02/26/2020
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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01/22/2020
Robust block preconditioners for poroelasticity
In this paper we study the linear systems arising from discretized poroe...
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11/23/2019
Constrained Linear Data-feature Mapping for Image Classification
In this paper, we propose a constrained linear data-feature mapping mode...
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10/03/2019
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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08/22/2019
Extended Galerkin Method
A general framework, known as extended Galerkin method, is presented in ...
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04/04/2019
On the Approximation Properties of Neural Networks
We prove two new results concerning the approximation properties of neur...
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01/29/2019
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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07/11/2018