2023/11/26 by Tengyuan Chang, Gung‐Min Gie, Chang, Teng-Yuan +5 · 1 citation
Chemical Engineering · Engineering · Physics and Astronomy · #65M99 #68T99 #68U99 #76D05 #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Rheology and Fluid Dynamics Studies
paper · pdf · doi:10.48550/arxiv.2311.15304
openalex publication_date 2023/11/26 · openalex created_date 2023/11/29 · openalex updated_date 2026/07/28
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 stiff solutions of plane-parallel flows at a small viscosity. Recalling the boundary layer analysis, we first find the corrector for the problem which describes the singular behavior of the viscous flow inside boundary layers. Then, using the components of the corrector and its curl, we build our new \em sl-PINN predictions for the velocity and the vorticity by either embedding the explicit expression of the corrector (or its curl) in the structure of PINNs or by training the implicit parts of the corrector (or its curl) together with the PINN predictions. Numerical experiments confirm that our new \em sl-PINNs produce stable and accurate predicted solutions for the plane-parallel flows at a small viscosity.