Application of PINN to obtain solution of boundary layer problems arising in fluid dynamics

In this article, we address the challenge of solving two-parameter singular perturbation problems in fluid dynamics, which often exhibit boundary layers. These problems are crucial in various fields, including fluid and gas dynamics, where complex interactions between fluid flow and boundary layers pose significant computational challenges. Standard physics-informed neural networks (PINNs) have been shown to struggle with such problems due to their inability to accurately capture boundary layers. Building on recent advancements, we implement a modified version of PINNs, known as finite basis physics-informed neural networks (FB-PINNs), inspired by classical finite element methods. Our work provides a comparative study between FB-PINNs and standard PINNs, evaluating their performance in solving two-parameter singular perturbation problems with boundary layers. We demonstrate that FB-PINNs offer superior accuracy and efficiency, particularly in handling multi-scale solutions without requiring prior knowledge of layer structures.