Posteriori error neural network: a recovery type posteriori error estimator based on neural network for diffusion problems

Boundary value problems for second-order elliptic equations (35J25) Finite element methods applied to problems in solid mechanics (74S05) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35)

Cites Work

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Guaranteed and fully robust a posteriori error estimates for conforming discretizations of diffusion problems with discontinuous coefficients
Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection-diffusion-reaction problems
Flux reconstruction and a posteriori error estimation for discontinuous Galerkin methods on general nonmatching grids
A posteriori error estimation and adaptive mesh-refinement techniques
Adaptive finite element methods for elliptic equations with non-smooth coefficients
Multilayer feedforward networks are universal approximators
Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems
Adversarial uncertainty quantification in physics-informed neural networks
Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems
Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Recovery-Based Error Estimator for Interface Problems: Conforming Linear Elements
A simple error estimator and adaptive procedure for practical engineerng analysis
A‐posteriori error estimates for the finite element method
Error Estimates for Adaptive Finite Element Computations
Explicit error bounds in a conforming finite element method
A Local A Posteriori Error Estimator Based on Equilibrated Fluxes
Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations
Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks
Approximations in elasticity based on the concept of function space
The generalized finite element method

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