Solving Poisson problems in polygonal domains with singularity enriched physics informed neural networks
DOI10.1137/23m1601195zbMATH Open1545.65478MaRDI QIDQ6585303
Zhi Zhou, Bangti Jin, Unnamed Author
Publication date: 9 August 2024
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
corner singularityPoisson equationedge singularityphysics informed neural networksingularity enrichment
Artificial neural networks and deep learning (68T07) Numerical optimization and variational techniques (65K10) Smoothness and regularity of solutions to PDEs (35B65) Boundary value problems for second-order elliptic equations (35J25) PDEs in connection with optics and electromagnetic theory (35Q60) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Singularity in context of PDEs (35A21) Numerical methods for partial differential equations, boundary value problems (65N99)
Cites Work
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- Weak adversarial networks for high-dimensional partial differential equations
- Bounds to eigenvalues of the Laplacian on L-shaped domain by variational methods
- On finite element methods for elliptic equations on domains with corners
- Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions
- Numerical solution to the time-dependent Maxwell equations in two-dimensional singular domains: The singular complement method
- The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
- DGM: a deep learning algorithm for solving partial differential equations
- Approximation rates for neural networks with encodable weights in smoothness spaces
- Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks
- Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs
- Least-squares ReLU neural network (LSNN) method for linear advection-reaction equation
- When and why PINNs fail to train: a neural tangent kernel perspective
- Scientific machine learning through physics-informed neural networks: where we are and what's next
- On the use of singular functions with finite element approximations
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- A finite element method using singular functions for Poisson equations: Mixed boundary conditions
- Greedy training algorithms for neural networks and applications to PDEs
- A Finite Element Method Using Singular Functions for the Poisson Equation: Corner Singularities
- On the mathematical foundations of learning
- Solution Methods for the Poisson Equation with Corner Singularities: Numerical Results
- Verified Eigenvalue Evaluation for the Laplacian over Polygonal Domains of Arbitrary Shape
- The extended/generalized finite element method: An overview of the method and its applications
- The post-processing approach in the finite element method—Part 2: The calculation of stress intensity factors
- Convergence rates for adaptive finite elements
- Singularities of the Laplacian at corners and edges of three-dimensional domains and their treatment with finite element methods
- Singularities of Corner Problems and Problems of Corner Singularities
- Approximations of Very Weak Solutions to Boundary-Value Problems
- 10.1162/153244303321897690
- A Limited Memory Algorithm for Bound Constrained Optimization
- Neural Network Learning
- Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning
- A Rate of Convergence of Physics Informed Neural Networks for the Linear Second Order Elliptic PDEs
- Imaging conductivity from current density magnitude using neural networks*
- On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs
- Physics-Informed Neural Networks with Hard Constraints for Inverse Design
- Approximations and Bounds for Eigenvalues of Elliptic Operators
- Estimates on the generalization error of physics-informed neural networks for approximating PDEs
- Singular solutions of the Poisson equation at edges of three‐dimensional domains and their treatment with a predictor–corrector finite element method
- Solving Elliptic Problems with Singular Sources Using Singularity Splitting Deep Ritz Method
- Deep Learning Solution of the Eigenvalue Problem for Differential Operators
- Error analysis of deep Ritz methods for elliptic equations
- Failure-Informed Adaptive Sampling for PINNs
- Error estimates for physics-informed neural networks approximating the Navier-Stokes equations
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