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A simple shallow neural network for emulating the solution to singularly perturbed problems
Christos Xenophontos, Aayushman Raina
We consider (feed-forward) Neural Networks (NNs) for the emulation of the solution to singularly perturbed second order boundary value problems, with two small parameters. We descr…
Error Analysis of a Fully-Discrete Implicit -Scheme with WG-FEM for Parabolic Singularly Perturbed Boundary Turning Point Problems
Aayushman Raina, Srinivasan Natesan
In this article, we introduce a weak Galerkin finite element method (WG-FEM) for a class of parabolic singularly perturbed boundary turning point problems (SPBTPPs). The proposed n…
A Parameter-Driven Physics-Informed Neural Network Framework for Solving Two-Parameter Singular Perturbation Problems Involving Boundary Layers
Pradanya Boro, Aayushman Raina, Srinivasan Natesan
In this article, our goal is to solve two-parameter singular perturbation problems (SPPs) in one- and two-dimensions using an adapted Physics-Informed Neural Networks (PINNs) appro…
Anisotropic Error Analysis of Weak Galerkin finite element method for Singularly Perturbed Biharmonic Problems
Aayushman Raina, Srinivasan Natesan, Şuayip Toprakseven
We consider the Weak Galerkin finite element approximation of the Singularly Perturbed Biharmonic elliptic problem on a unit square domain with clamped boundary conditions. Shishki…