Adaptive two-layer ReLU neural network. II: Ritz approximation to elliptic PDEs

DOI10.1016/j.camwa.2022.03.010OpenAlexW3179979867WikidataQ114201486 ScholiaQ114201486MaRDI QIDQ2122635

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/2107.06459

zbMATH Keywords

neural networkadaptivityRitz methoda posteriori estimatordiffusion-reaction problem

Mathematics Subject Classification ID

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

Related Items (5)

Adaptive two-layer ReLU neural network. I: Best least-squares approximation ⋮ Self-adaptive deep neural network: numerical approximation to functions and PDEs ⋮ A deep first-order system least squares method for solving elliptic PDEs ⋮ Deep Ritz method with adaptive quadrature for linear elasticity ⋮ 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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• Approximation by Ridge Functions and Neural Networks
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• Finite Neuron Method and Convergence Analysis
• Approximation by superpositions of a sigmoidal function

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