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math.NA2023
Semi-analytic PINN methods for boundary layer problems in a rectangular domain
Gung-Min Gie, Youngjoon Hong, Chang-Yeol Jung +1
Singularly perturbed boundary value problems pose a significant challenge for their numerical approximations because of the presence of sharp boundary layers. These sharp boundary…
math.NA2023
Singular Layer Physics-Informed Neural Network Method for Convection-Dominated Boundary Layer Problems in Two Dimensions
Gung-Min Gie, Youngjoon Hong, Chang-Yeol Jung +1
This research explores neural network-based numerical approximation of two-dimensional convection-dominated singularly perturbed problems on square, circular, and elliptic domains.…
math.NA2023
Singular layer Physics Informed Neural Network method for Plane Parallel Flows
Teng-Yuan Chang, Gung-Min Gie, Youngjoon Hong +1
We construct in this article the semi-analytic Physics Informed Neural Networks (PINNs), called {\em singular layer PINNs} (or {\em sl-PINNs}), that are suitable to predict the sti…