Multistep asymptotic pre-training strategy based on PINNs for solving steep boundary singular perturbation problems (Q6609750)

scientific article; zbMATH DE number 7917719

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English	Multistep asymptotic pre-training strategy based on PINNs for solving steep boundary singular perturbation problems	scientific article; zbMATH DE number 7917719

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instance of

scholarly article

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title

Multistep asymptotic pre-training strategy based on PINNs for solving steep boundary singular perturbation problems (English)

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Computer Methods in Applied Mechanics and Engineering

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publication date

24 September 2024

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zbMATH Keywords

asymptotic parameter strategy

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multiple time pre-training strategy

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singularly perturbed problem

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physics-informed neural networks

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Shishkin mesh simulation: a new stabilization technique for convection-diffusion problems

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Q4242861

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Discrete approximations of solutions and derivatives for a singularly perturbed parabolic convection--diffusion equation.

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Q3525497

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Finite element method on Shishkin mesh for a singularly perturbed problem with an interior layer

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Uniform convergence of a weak Galerkin finite element method on Shishkin mesh for singularly perturbed convection-diffusion problems in 2D

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Numerical treatment of a singularly perturbed 2-D convection-diffusion elliptic problem with Robin-type boundary conditions

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A method of line with improved accuracy for singularly perturbed parabolic convection-diffusion problems with large temporal lag

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An efficient numerical approach for singularly perturbed parabolic convection-diffusion problems with large time-lag

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Q5884054

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A higher order numerical scheme for singularly perturbed parabolic turning point problems exhibiting twin boundary layers

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A parameter uniform higher order scheme for 2D singularly perturbed parabolic convection-diffusion problem with turning point

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A splitting uniformly convergent method for one-dimensional parabolic singularly perturbed convection-diffusion systems

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Uniformly convergent NIPG method for singularly perturbed convection diffusion problem on Shishkin type meshes

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A novel two-step streamline-diffusion FEM for singularly perturbed 2D parabolic PDEs

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DGM: a deep learning algorithm for solving partial differential equations

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The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems

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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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Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems

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Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations

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Parallel physics-informed neural networks via domain decomposition

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PPINN: parareal physics-informed neural network for time-dependent PDEs

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Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations

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Deep neural networks based temporal-difference methods for high-dimensional parabolic partial differential equations

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Adaptive deep neural networks methods for high-dimensional partial differential equations

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Weak adversarial networks for high-dimensional partial differential equations

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A-PINN: auxiliary physics informed neural networks for forward and inverse problems of nonlinear integro-differential equations

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Neural-PDE: a RNN based neural network for solving time dependent PDEs

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Pre-training strategy for solving evolution equations based on physics-informed neural networks

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

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Difference schemes on uniform grids for an initial-boundary value problem for a singularly perturbed parabolic convection-diffusion equation

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Exponential compact ADI method for a coupled system of convection-diffusion equations arising from the 2D unsteady magnetohydrodynamic (MHD) flows

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Identifiers

Mathematics Subject Classification ID

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10.1016/J.CMA.2024.117222

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Mathematics(1 entry)

mardi Publication:6609750