Multi-level neural networks for accurate solutions of boundary-value problems
From MaRDI portal
Publication:6185225
DOI10.1016/j.cma.2023.116666arXiv2308.11503MaRDI QIDQ6185225
Marc Laforest, Ziad Aldirany, Régis Cottereau, Serge Prudhomme
Publication date: 29 January 2024
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2308.11503
convergenceneural networkspartial differential equationsfrequency analysisnumerical errorphysics-informed neural networks
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Weak adversarial networks for high-dimensional partial differential equations
- The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
- A posteriori error estimation and error control for finite element approximations of the time-dependent Navier--Stokes equations
- DGM: a deep learning algorithm for solving partial differential equations
- NSFnets (Navier-Stokes flow nets): physics-informed neural networks for the incompressible Navier-Stokes equations
- Physics-informed neural networks for the shallow-water equations on the sphere
- A new goal-oriented formulation of the finite element method
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- On a goal-oriented version of the proper generalized decomposition method
- A Posteriori Error Estimates Based on Hierarchical Bases
- Galerkin Neural Networks: A Framework for Approximating Variational Equations with Error Control
- Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains
- Approximation by superpositions of a sigmoidal function
- Goal-oriented error estimation and adaptivity for the finite element method
This page was built for publication: Multi-level neural networks for accurate solutions of boundary-value problems
