Finite element interpolated neural networks for solving forward and inverse problems
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Publication:6118570
DOI10.1016/j.cma.2023.116505arXiv2306.06304OpenAlexW4387443591MaRDI QIDQ6118570
Wei Li, Santiago Badia, Alberto F. Martín
Publication date: 21 March 2024
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2306.06304
Cites Work
- Unnamed Item
- A posteriori error estimation in finite element analysis
- A second-order-accurate symmetric discretization of the Poisson equation on irregular domains
- The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
- Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks
- Hybrid FEM-NN models: combining artificial neural networks with the finite element method
- On quadrature rules for solving partial differential equations using neural networks
- Variational physics informed neural networks: the role of quadratures and test functions
- Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data
- A tutorial on the adjoint method for inverse problems
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- The software design of gridap: a finite element package based on the Julia JIT compiler
- A penalty method for PDE-constrained optimization in inverse problems
- Composing Scalable Nonlinear Algebraic Solvers
- Preconditioning discretizations of systems of partial differential equations
- Finite element exterior calculus, homological techniques, and applications
- Multilevel Balancing Domain Decomposition at Extreme Scales
- Optimization with PDE Constraints
- Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities
- A Comparison Study of Deep Galerkin Method and Deep Ritz Method for Elliptic Problems with Different Boundary Conditions
- Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations
- Scheduling Massively Parallel Multigrid for Multilevel Monte Carlo Methods
- Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential equations
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