An accurate and efficient continuity-preserved method based on randomized neural networks for elliptic interface problems

DOI10.1137/24m1632309MaRDI QIDQ6623701

Jinyong Ying, Jiao Li, Zuoshunhua Shi, Jingying Hu

Publication date: 24 October 2024

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

zbMATH Keywords

error estimatemultilevel methodelliptic interface problemsrandomized neural networkscontinuity preserved method

Mathematics Subject Classification ID

Computational learning theory (68Q32) Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Artificial neural networks and deep learning (68T07) Numerical optimization and variational techniques (65K10) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Nonlinear elliptic equations (35J60) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Numerical methods for partial differential equations, boundary value problems (65N99) Preconditioners for iterative methods (65F08)

Cites Work

• Unnamed Item
• Unnamed Item
• Automated solution of differential equations by the finite element method. The FEniCS book
• The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
• Approximation rates for neural networks with general activation functions
• Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems
• Local extreme learning machines and domain decomposition for solving linear and nonlinear partial differential equations
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• A discontinuity capturing shallow neural network for elliptic interface problems
• Multi-scale fusion network: a new deep learning structure for elliptic interface problems
• Greedy training algorithms for neural networks and applications to PDEs
• High-Dimensional Statistics
• A Subspace, Interior, and Conjugate Gradient Method for Large-Scale Bound-Constrained Minimization Problems
• Two-Grid Discretization Techniques for Linear and Nonlinear PDE<scp>s</scp>
• Deep Unfitted Nitsche Method for Elliptic Interface Problems
• A Rate of Convergence of Physics Informed Neural Networks for the Linear Second Order Elliptic PDEs
• Convergence of Physics-Informed Neural Networks Applied to Linear Second-Order Elliptic Interface Problems
• A cusp-capturing PINN for elliptic interface problems
• Numerical computation of partial differential equations by hidden-layer concatenated extreme learning machine
• Failure-Informed Adaptive Sampling for PINNs

This page was built for publication: An accurate and efficient continuity-preserved method based on randomized neural networks for elliptic interface problems