Generalization error in the deep Ritz method with smooth activation functions
DOI10.4208/cicp.oa-2023-0253MaRDI QIDQ6585908
Publication date: 12 August 2024
Published in: Communications in Computational Physics (Search for Journal in Brave)
Artificial neural networks and deep learning (68T07) Monte Carlo methods (65C05) Numerical optimization and variational techniques (65K10) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Theoretical approximation in context of PDEs (35A35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for partial differential equations, boundary value problems (65N99)
Cites Work
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- Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
- Multilayer feedforward networks are universal approximators
- The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
- DGM: a deep learning algorithm for solving partial differential equations
- Rademacher complexity and the generalization error of residual networks
- A priori and a posteriori error estimates for the deep Ritz method applied to the Laplace and Stokes problem
- Uniform convergence guarantees for the deep Ritz method for nonlinear problems
- The Barron space and the flow-induced function spaces for neural network models
- Scientific machine learning through physics-informed neural networks: where we are and what's next
- A priori estimates of the population risk for two-layer neural networks
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- On the approximate calculation of multiple integrals
- Numerical Analysis of a Finite Element/Volume Penalty Method
- Universal approximation bounds for superpositions of a sigmoidal function
- A Singularly mixed boundary value problem
- Neural Network Learning
- A multi-level procedure for enhancing accuracy of machine learning algorithms
- Convergence Rate Analysis for Deep Ritz Method
- DeepXDE: A Deep Learning Library for Solving Differential Equations
- On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs
- Understanding Machine Learning
- A Local Deep Learning Method for Solving High Order Partial Differential Equations
- Solving Elliptic Problems with Singular Sources Using Singularity Splitting Deep Ritz Method
- Error analysis of deep Ritz methods for elliptic equations
- Convergence Analysis of a Quasi-Monte CarloBased Deep Learning Algorithm for Solving Partial Differential Equations
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