Adaptive two-layer ReLU neural network. I: Best least-squares approximation

DOI10.1016/j.camwa.2022.03.005zbMath1504.65275arXiv2107.08935OpenAlexW3183891129MaRDI QIDQ2122629

Jingshuang Chen, Min Liu, Zhi-qiang Cai

Publication date: 7 April 2022

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2107.08935

zbMATH Keywords

neural networkadaptivityleast-squares approximationReLU activation

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Numerical methods for partial differential equations, boundary value problems (65N99)

Related Items (8)

Adaptive two-layer ReLU neural network. II: Ritz approximation to elliptic PDEs ⋮ Self-adaptive deep neural network: numerical approximation to functions and PDEs ⋮ Least-squares ReLU neural network (LSNN) method for scalar nonlinear hyperbolic conservation law ⋮ Neural control of discrete weak formulations: Galerkin, least squares \& minimal-residual methods with quasi-optimal weights ⋮ A deep first-order system least squares method for solving elliptic PDEs ⋮ Deep Ritz method with adaptive quadrature for linear elasticity ⋮ Deep nonparametric estimation of intrinsic data structures by chart autoencoders: generalization error and robustness ⋮ Least-squares neural network (LSNN) method for scalar nonlinear hyperbolic conservation laws: discrete divergence operator

Uses Software

• Adam
• DGM

Cites Work

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• Optimization Methods for Large-Scale Machine Learning
• Convergence of Adaptive Finite Element Methods
• High-dimensional integration: The quasi-Monte Carlo way
• Approximation by superpositions of a sigmoidal function

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