Robust variational physics-informed neural networks
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Publication:6497138
DOI10.1016/J.CMA.2024.116904MaRDI QIDQ6497138
Maciej Paszynski, David Pardo, Sergio Rojas, Paweł Maczuga, Judit Muñoz-Matute
Publication date: 6 May 2024
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
robustnessa posteriori error estimationRiesz representationPetrov-Galerkin formulationminimum residual principlevariational physics-informed neural networks
Cites Work
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- The DPG method for the Stokes problem
- A converse to Fortin's lemma in Banach spaces
- Mathematical aspects of discontinuous Galerkin methods.
- A class of discontinuous Petrov-Galerkin methods. I: The transport equation
- An optimal Poincaré inequality for convex domains
- A new finite element formulation for computational fluid dynamics. VIII. The Galerkin/least-squares method for advective-diffusive equations
- Least-squares finite element methods
- Construction of DPG Fortin operators for second order problems
- Isogeometric residual minimization method (iGRM) with direction splitting for non-stationary advection-diffusion problems
- Isogeometric residual minimization method (iGRM) with direction splitting preconditioner for stationary advection-dominated diffusion problems
- A DPG-based time-marching scheme for linear hyperbolic problems
- \textit{hp}-VPINNs: variational physics-informed neural networks with domain decomposition
- Goal-oriented adaptivity for a conforming residual minimization method in a dual discontinuous Galerkin norm
- Isogeometric residual minimization (iGRM) for non-stationary Stokes and Navier-Stokes problems
- Physics-informed graph neural Galerkin networks: a unified framework for solving PDE-governed forward and inverse problems
- Solving PDEs by variational physics-informed neural networks: an a posteriori error analysis
- Variational physics informed neural networks: the role of quadratures and test functions
- Physics-informed neural networks for high-speed flows
- Automatically adaptive, stabilized finite element method via residual minimization for heterogeneous, anisotropic advection-diffusion-reaction problems
- An adaptive stabilized conforming finite element method via residual minimization on dual discontinuous Galerkin norms
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Least-squares ReLU neural network (LSNN) method for scalar nonlinear hyperbolic conservation law
- Neural control of discrete weak formulations: Galerkin, least squares \& minimal-residual methods with quasi-optimal weights
- A deep Fourier residual method for solving PDEs using neural networks
- A deep double Ritz method (\(\mathrm{D^2RM}\)) for solving partial differential equations using neural networks
- Robust DPG Method for Convection-Dominated Diffusion Problems
- An analysis of the convergence of mixed finite element methods
- First-Order System Least Squares for Second-Order Partial Differential Equations: Part I
- First-Order System Least Squares for Second-Order Partial Differential Equations: Part II
- An optimal Poincaré inequality in $L^1$ for convex domains
- Mixed Finite Element Methods and Applications
- Galerkin Neural Networks: A Framework for Approximating Variational Equations with Error Control
- Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs
- An Overview of the Discontinuous Petrov Galerkin Method
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