Less Emphasis on Hard Regions: Curriculum Learning of PINNs for Singularly Perturbed Convection-Diffusion-Reaction Problems

DOI10.4208/eajam.2023-062.170523zbMath1530.35298arXiv2210.12685OpenAlexW4389752819MaRDI QIDQ6192635

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Publication date: 13 February 2024

Published in: Unnamed Author (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2210.12685

zbMATH Keywords

boundary layerinterior layerconvection-diffusion-reactioncurriculum learningphysics-informed neural network

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Approximation algorithms (68W25) PDEs in connection with computer science (35Q68)

Cites Work

• Analysis of SDFEM on Shishkin triangular meshes and hybrid meshes for problems with characteristic layers
• Theory-guided physics-informed neural networks for boundary layer problems with singular perturbation
• When and why PINNs fail to train: a neural tangent kernel perspective
• Normalizing field flows: solving forward and inverse stochastic differential equations using physics-informed flow models
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• A multiscale discontinuous Galerkin method with the computational structure of a continuous Galerkin method
• Kolmogorov n-width and Lagrangian physics-informed neural networks: a causality-conforming manifold for convection-dominated PDEs
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems
• The SDFEM for a Convection-Diffusion Problem with a Boundary Layer: Optimal Error Analysis and Enhancement of Accuracy
• Convergence and supercloseness of a finite element method for a singularly perturbed convection–diffusion problem on an L-shaped domain
• Semiconductor device modelling from the numerical point of view
• Solving high-dimensional partial differential equations using deep learning
• Physics-Driven Learning of the Steady Navier-Stokes Equations using Deep Convolutional Neural Networks
• An Augmented Lagrangian Deep Learning Method for Variational Problems with Essential Boundary Conditions
• A Deep Learning Method for Elliptic Hemivariational Inequalities
• Deep Unfitted Nitsche Method for Elliptic Interface Problems
• DeepXDE: A Deep Learning Library for Solving Differential Equations
• Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks
• Optimal Order $L^2$ Error Estimate of SDFEM on Shishkin Triangular Meshes for Singularly Perturbed Convection-Diffusion Equations
• Convergence of Physics-Informed Neural Networks Applied to Linear Second-Order Elliptic Interface Problems
• Failure-Informed Adaptive Sampling for PINNs
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