DNN-HDG: a deep learning hybridized discontinuous Galerkin method for solving some elliptic problems

DOI10.1016/j.enganabound.2023.03.039zbMath1521.74205OpenAlexW4362508031MaRDI QIDQ6158712

F. Mostajeran, Shima Baharlouei, Reza Mokhtari

Publication date: 20 June 2023

Published in: Engineering Analysis with Boundary Elements (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.enganabound.2023.03.039

zbMATH Keywords

elliptic problemshybridized discontinuous Galerkin methoddeep neural networks

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Finite element methods applied to problems in solid mechanics (74S05) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

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Cites Work

• Unnamed Item
• Weak adversarial networks for high-dimensional partial differential equations
• Multilayer feedforward networks are universal approximators
• The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
• PPINN: parareal physics-informed neural network for time-dependent PDEs
• \textit{hp}-VPINNs: variational physics-informed neural networks with domain decomposition
• A stable numerical scheme based on the hybridized discontinuous Galerkin method for the Ito-type coupled KdV system
• Numerical study of simultaneous growth of multiple hydraulic fractures from a horizontal wellbore combining dual boundary element method and finite volume method
• MIM: a deep mixed residual method for solving high-order partial differential equations
• A mesh-free method using piecewise deep neural network for elliptic interface problems
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Uncertainty Quantification for Hyperbolic Systems of Conservation Laws
• A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• A Characterization of Hybridized Mixed Methods for Second Order Elliptic Problems
• Hybridizable discontinuous Galerkin p‐adaptivity for wave propagation problems
• Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning
• MOD-Net: A Machine Learning Approach via Model-Operator-Data Network for Solving PDEs
• Numerical solution of inverse problems by weak adversarial networks
• Machine Learning and Computational Mathematics
• Local Discontinuous Galerkin Methods for the Degasperis-Procesi Equation
• A logical calculus of the ideas immanent in nervous activity
• A cell-based smoothed finite element method for multi-body contact analysis within the bi-potential formulation
• DeepBHCP: deep neural network algorithm for solving backward heat conduction problems

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