Analysis of deep Ritz methods for semilinear elliptic equations (Q6662390)

scientific article; zbMATH DE number 7966425

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English	Analysis of deep Ritz methods for semilinear elliptic equations	scientific article; zbMATH DE number 7966425

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instance of

scholarly article

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title

Analysis of deep Ritz methods for semilinear elliptic equations (English)

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Numerical Mathematics: Theory, Methods and Applications

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publication date

14 January 2025

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zbMATH Keywords

semilinear elliptic equations

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deep Ritz method

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ReLU\(^2\) ResNet

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convergence rate

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MaRDI profile type

Publication

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cites work

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A priori generalization error analysis of two-layer neural networks for solving high dimensional Schrödinger eigenvalue problems

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Numerical Analysis of a Finite Element/Volume Penalty Method

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Deep Nitsche Method: Deep Ritz Method with Essential Boundary Conditions

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Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs

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Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

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Nonlinear partial differential equations with applications

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Estimations des erreurs de meilleure approximation polynomiale et d'interpolation de Lagrange dans les espaces de Sobolev d'ordre non entier. (Estimation of the best polynomial approximation error and the Lagrange interpolation error in fractional-order Sobolev spaces)

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DGM: a deep learning algorithm for solving partial differential equations

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Nesting Monte Carlo for high-dimensional non-linear PDEs

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Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations

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Weak adversarial networks for high-dimensional partial differential equations

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Identifiers

Mathematics Subject Classification ID

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10.4208/NMTMA.OA-2023-0058

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Sitelinks

Mathematics(1 entry)

mardi Publication:6662390