Less Emphasis on Hard Regions: Curriculum Learning of PINNs for Singularly Perturbed Convection-Diffusion-Reaction Problems (Q6192635)

scientific article; zbMATH DE number 7803730

Language	Label	Description	Also known as
English	Less Emphasis on Hard Regions: Curriculum Learning of PINNs for Singularly Perturbed Convection-Diffusion-Reaction Problems	scientific article; zbMATH DE number 7803730

Statements

instance of

scholarly article

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title

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

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published in

East Asian Journal on Applied Mathematics

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publication date

13 February 2024

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full work available at URL

https://arxiv.org/abs/2210.12685

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zbMATH Keywords

physics-informed neural network

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convection-diffusion-reaction

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boundary layer

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interior layer

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curriculum learning

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MaRDI profile type

MaRDI publication profile

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cites work

Theory-guided physics-informed neural networks for boundary layer problems with singular perturbation

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Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems

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Q3896757

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Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks

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Failure-Informed Adaptive Sampling for PINNs

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Deep Unfitted Nitsche Method for Elliptic Interface Problems

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Normalizing field flows: solving forward and inverse stochastic differential equations using physics-informed flow models

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Solving high-dimensional partial differential equations using deep learning

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A Deep Learning Method for Elliptic Hemivariational Inequalities

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

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A multiscale discontinuous Galerkin method with the computational structure of a continuous Galerkin method

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DeepXDE: A Deep Learning Library for Solving Differential Equations

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Convergence and supercloseness of a finite element method for a singularly perturbed convection–diffusion problem on an L-shaped domain

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Physics-Driven Learning of the Steady Navier-Stokes Equations using Deep Convolutional Neural Networks

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Q4379541

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Kolmogorov n-width and Lagrangian physics-informed neural networks: a causality-conforming manifold for convection-dominated PDEs

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Semiconductor device modelling from the numerical point of view

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Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

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Robust Numerical Methods for Singularly Perturbed Differential Equations

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The SDFEM for a Convection-Diffusion Problem with a Boundary Layer: Optimal Error Analysis and Enhancement of Accuracy

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When and why PINNs fail to train: a neural tangent kernel perspective

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Convergence of Physics-Informed Neural Networks Applied to Linear Second-Order Elliptic Interface Problems

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Analysis of SDFEM on Shishkin triangular meshes and hybrid meshes for problems with characteristic layers

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Optimal Order $L^2$ Error Estimate of SDFEM on Shishkin Triangular Meshes for Singularly Perturbed Convection-Diffusion Equations

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Identifiers

zbMATH Open document ID

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10.4208/eajam.2023-062.170523

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:6192635