Convergence Analysis of the Deep Galerkin Method for Weak Solutions

DOI10.1007/978-3-031-37800-3_4arXiv2302.02405OpenAlexW4387915855MaRDI QIDQ6194482

Yunfei Yang, Haizhao Yang, Yan-Ming Lai, Yang Wang, Yu Ling Jiao

Publication date: 19 March 2024

Published in: Applied and Numerical Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2302.02405

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Boundary value problems for second-order elliptic equations (35J25) Weak solutions to PDEs (35D30)

Cites Work

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• Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
• Weak adversarial networks for high-dimensional partial differential equations
• The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
• Weak convergence and empirical processes. With applications to statistics
• Approximation rates for neural networks with general activation functions
• DGM: a deep learning algorithm for solving partial differential equations
• Approximation rates for neural networks with encodable weights in smoothness spaces
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• A Rate of Convergence of Physics Informed Neural Networks for the Linear Second Order Elliptic PDEs
• Understanding Machine Learning

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