De Rham compatible deep neural network FEM
From MaRDI portal
Publication:6057971
DOI10.1016/j.neunet.2023.06.008arXiv2201.05395OpenAlexW4380078591MaRDI QIDQ6057971
Marcello Longo, Nico Disch, Christoph Schwab, J. Zech, Joost A. A. Opschoor
Publication date: 26 October 2023
Published in: Neural Networks (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2201.05395
Artificial neural networks and deep learning (68T07) Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) de Rham theory in global analysis (58A12)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Regularity of minimizers of integrals of the calculus of variations with non-standard growth conditions
- A coercive bilinear form for Maxwell's equations
- Boundary element methods for Maxwell transmission problems in Lipschitz domains
- The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
- Orientation embedded high order shape functions for the exact sequence elements of all shapes
- Exponential ReLU DNN expression of holomorphic maps in high dimension
- B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data
- Enforcing exact physics in scientific machine learning: a data-driven exterior calculus on graphs
- Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap
- Optimal approximation of piecewise smooth functions using deep ReLU neural networks
- Crouzeix-Raviart approximation of the total variation on simplicial meshes
- Multipatch approximation of the de Rham sequence and its traces in isogeometric analysis
- Error bounds for approximations with deep ReLU networks
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Deep vs. shallow networks: An approximation theory perspective
- Relu Deep Neural Networks and Linear Finite Elements
- Singularities of Maxwell interface problems
- Nonconforming Finite Elements for the Stokes Problem
- Vector potentials in three-dimensional non-smooth domains
- An optimal domain decomposition preconditioner for low-frequency time-harmonic Maxwell equations
- Maxwell and Lamé eigenvalues on polyhedra
- Deep learning in high dimension: Neural network expression rates for generalized polynomial chaos expansions in UQ
- Hybrid High-Order Methods
- Finite Elements I
- PowerNet: Efficient Representations of Polynomials and Smooth Functions by Deep Neural Networks with Rectified Power Units
- Finite element quasi-interpolation and best approximation
- Boundary Element Methods
- ReLU neural network Galerkin BEM
This page was built for publication: De Rham compatible deep neural network FEM
