Domain decomposition learning methods for solving elliptic problems
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Publication:6585310
DOI10.1137/22m1515392zbMATH Open1545.65473MaRDI QIDQ6585310
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Publication date: 9 August 2024
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Artificial neural networks and deep learning (68T07) Boundary value problems for second-order elliptic equations (35J25) Neural networks for/in biological studies, artificial life and related topics (92B20) Variational methods applied to PDEs (35A15)
Cites Work
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- Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
- Weak adversarial networks for high-dimensional partial differential equations
- Domain decomposition methods for the numerical solution of partial differential equations
- Multilayer feedforward networks are universal approximators
- The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
- DGM: a deep learning algorithm for solving partial differential equations
- Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks
- INN: interfaced neural networks as an accessible meshless approach for solving interface PDE problems
- A deep domain decomposition method based on Fourier features
- A mesh-free method using piecewise deep neural network for elliptic interface problems
- Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Improved deep neural networks with domain decomposition in solving partial differential equations
- Machine Learning for Fluid Mechanics
- Combining Machine Learning and Adaptive Coarse Spaces---A Hybrid Approach for Robust FETI-DP Methods in Three Dimensions
- An Iterative Procedure with Interface Relaxation for Domain Decomposition Methods
- Some Nonoverlapping Domain Decomposition Methods
- Finite Volume Methods for Hyperbolic Problems
- Optimization Methods for Large-Scale Machine Learning
- Minimal regularity of the solutions of some transmission problems
- Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks
- When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?
- PFNN-2: A Domain Decomposed Penalty-Free Neural Network Method for Solving Partial Differential Equations
- An Augmented Lagrangian Deep Learning Method for Variational Problems with Essential Boundary Conditions
- A Comparison Study of Deep Galerkin Method and Deep Ritz Method for Elliptic Problems with Different Boundary Conditions
- Machine Learning in Adaptive FETI-DP: Reducing the Effort in Sampling
- Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks
- Deep Nitsche Method: Deep Ritz Method with Essential Boundary Conditions
- The Mathematical Theory of Finite Element Methods
- The Immersed Interface Method
- On the Optimal Convergence Rate of a Robin-Robin Domain Decomposition Method
- The Monte Carlo Method
- Combining machine learning and domain decomposition methods for the solution of partial differential equations—A review
- Failure-Informed Adaptive Sampling for PINNs
- Predicting the geometric location of critical edges in adaptive GDSW overlapping domain decomposition methods using deep learning
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