WAN discretization of PDEs: best approximation, stabilization, and essential boundary conditions
DOI10.1137/23m1588196MaRDI QIDQ6660351
Silvia Bertoluzza, Cuiyu He, Erik Burman
Publication date: 10 January 2025
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Artificial neural networks and deep learning (68T07) Numerical optimization and variational techniques (65K10) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Weak solutions to PDEs (35D30) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) PDEs on manifolds (35R01) Systems of nonlinear higher-order PDEs (35G50)
Cites Work
- Unnamed Item
- Unnamed Item
- Weak adversarial networks for high-dimensional partial differential equations
- Data assimilation for the heat equation using stabilized finite element methods
- Theory and practice of finite elements.
- Topological properties of the set of functions generated by neural networks of fixed size
- Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks
- Simulator-free solution of high-dimensional stochastic elliptic partial differential equations using deep neural networks
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Adaptive deep neural networks methods for high-dimensional partial differential equations
- Towards fast weak adversarial training to solve high dimensional parabolic partial differential equations using XNODE-WAN
- Neural‐network‐based approximations for solving partial differential equations
- Space time stabilized finite element methods for a unique continuation problem subject to the wave equation
- Convergence Rate Analysis for Deep Ritz Method
- Error bounds for approximations with deep ReLU neural networks in Ws,p norms
- Numerical solution of inverse problems by weak adversarial networks
- $\phi$-FEM: A Finite Element Method on Domains Defined by Level-Sets
- Nonclosedness of sets of neural networks in Sobolev spaces
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