Deep Ritz method with adaptive quadrature for linear elasticity (Q6096475)

scientific article; zbMATH DE number 7736342

Language	Label	Description	Also known as
English	Deep Ritz method with adaptive quadrature for linear elasticity	scientific article; zbMATH DE number 7736342

Statements

instance of

scholarly article

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title

Deep Ritz method with adaptive quadrature for linear elasticity (English)

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Computer Methods in Applied Mechanics and Engineering

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publication date

12 September 2023

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full work available at URL

https://arxiv.org/abs/2305.15257

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zbMATH Keywords

deep neural network

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PDE

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linear elasticity

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deep Ritz

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adaptive quadrature

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MaRDI profile type

MaRDI publication profile

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cites work

Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks

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PDE-Net 2.0: learning PDEs from data with a numeric-symbolic hybrid deep network

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SwitchNet: A Neural Network Model for Forward and Inverse Scattering Problems

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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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DGM: a deep learning algorithm for solving partial differential equations

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The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems

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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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Deep least-squares methods: an unsupervised learning-based numerical method for solving elliptic PDEs

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Least-squares ReLU neural network (LSNN) method for linear advection-reaction equation

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A physics-guided neural network framework for elastic plates: comparison of governing equations-based and energy-based approaches

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

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Least-squares ReLU neural network (LSNN) method for scalar nonlinear hyperbolic conservation law

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Least-squares neural network (LSNN) method for scalar nonlinear hyperbolic conservation laws: discrete divergence operator

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Finite Neuron Method and Convergence Analysis

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

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Least-squares finite element methods

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Least-Squares Methods for Linear Elasticity

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Least-squares methods for elasticity and Stokes equations with weakly imposed symmetry

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A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics

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Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. (On a variational principle for solving Dirichlet problems less boundary conditions using subspaces)

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Deep Nitsche Method: Deep Ritz Method with Essential Boundary Conditions

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A deep double Ritz method ($\mathrm{D^2RM}$) for solving partial differential equations using neural networks

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Korn's inequalities for piecewise $H^1$ vector fields

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On quadrature rules for solving partial differential equations using neural networks

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Q4938227

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Approximation by superpositions of a sigmoidal function

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Multilayer feedforward networks are universal approximators

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Q3895980

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Q4162607

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Lowest-order weak Galerkin finite element methods for linear elasticity on rectangular and brick meshes

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Matlab implementation of the finite element method in elasticity

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CAN-PINN: a fast physics-informed neural network based on coupled-automatic-numerical differentiation method

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Identifiers

arXiv ID

2305.15257

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Mathematics Subject Classification ID

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10.1016/J.CMA.2023.116229

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Sitelinks

Mathematics(1 entry)

mardi Publication:6096475