An Augmented Lagrangian Deep Learning Method for Variational Problems with Essential Boundary Conditions

DOI10.4208/cicp.OA-2021-0176zbMath1482.65226arXiv2106.14348OpenAlexW3174598394MaRDI QIDQ5065200

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Publication date: 18 March 2022

Published in: Communications in Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.14348

zbMATH Keywords

saddle point problemsvariational problemsaugmented Lagrangian methoddeep learningessential boundary conditions

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Numerical methods for partial differential equations, boundary value problems (65N99)

Related Items (9)

A-PINN: auxiliary physics informed neural networks for forward and inverse problems of nonlinear integro-differential equations ⋮ Solving Time Dependent Fokker-Planck Equations via Temporal Normalizing Flow ⋮ A Chebyshev Polynomial Neural Network Solver for Boundary Value Problems of Elliptic Equations ⋮ A Hybrid Method for Three-Dimensional Semi-Linear Elliptic Equations ⋮ Failure-Informed Adaptive Sampling for PINNs ⋮ Feature engineering with regularity structures ⋮ An Adaptive Physics-Informed Neural Network with Two-Stage Learning Strategy to Solve Partial Differential Equations ⋮ Less Emphasis on Hard Regions: Curriculum Learning of PINNs for Singularly Perturbed Convection-Diffusion-Reaction Problems ⋮ Monte Carlo fPINNs: deep learning method for forward and inverse problems involving high dimensional fractional partial differential equations

Uses Software

• Adam
• DGM
• MscaleDNN

Cites Work

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