155 citations · 987 across the 104 of their papers we have counts for
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Approximation Rates for Shallow ReLU Neural Networks on Sobolev Spaces via the Radon Transform
Tong Mao, Jonathan W. Siegel, Jinchao Xu
Let be a bounded domain. We consider the problem of how efficiently shallow neural networks with the ReLU activation function can approximate functions…
Randomized Greedy Algorithms for Neural Network Optimization
Jinchao Xu, Xiaofeng Xu
Greedy algorithms have been successfully analyzed and applied in training neural networks for solving variational problems, ensuring guaranteed convergence orders. In this paper, w…
A Unified-Field Monolithic Fictitious Domain-Finite Element Method for Fluid-Structure-Contact Interactions and Applications to Deterministic Lateral Displacement Problems
Cheng Wang, Pengtao Sun, Yumiao Zhang +3
Based upon two overlapped, body-unfitted meshes, a type of unified-field monolithic fictitious domain-finite element method (UFMFD-FEM) is developed in this paper for moving interf…
Expressivity and Approximation Properties of Deep Neural Networks with ReLU Activation
Juncai He, Tong Mao, Jinchao Xu
In this paper, we investigate the expressivity and approximation properties of deep neural networks employing the ReLU activation function for . Although deep ReLU ne…
Deep Neural Networks and Finite Elements of Any Order on Arbitrary Dimensions
Juncai He, Jinchao Xu
In this study, we establish that deep neural networks employing ReLU and ReLU activation functions can effectively represent Lagrange finite element functions of any order on v…