Semi-analytic PINN methods for boundary layer problems in a rectangular domain

Artificial intelligence (68Txx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Qualitative properties of solutions to partial differential equations (35Bxx)

Cites Work

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Recent progresses in boundary layer theory
Enriched finite volume approximations of the plane-parallel flow at a small viscosity
Hidden physics models: machine learning of nonlinear partial differential equations
Singular perturbations and boundary layers
Analysis of mixed elliptic and parabolic boundary layers with corners
DGM: a deep learning algorithm for solving partial differential equations
\textit{hp}-VPINNs: variational physics-informed neural networks with domain decomposition
Semi-analytic shooting methods for Burgers' equation
Theory-guided physics-informed neural networks for boundary layer problems with singular perturbation
Deep neural network modeling of unknown partial differential equations in nodal space
On boundary layers for the Burgers equations in a bounded domain
On the numerical approximations of stiff convection-diffusion equations in a circle
Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Singularly perturbed reaction–diffusion equations in a circle with numerical applications
Singularly Perturbed Linear Two-Point Boundary Value Problems
Asymptotic Analysis of a Singular Perturbation Problem
Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks
Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations
Three ways to solve partial differential equations with neural networks — A review
Semi‐analytic time differencing methods for singularly perturbed initial value problems
Physics-informed neural networks and functional interpolation for stiff chemical kinetics

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