Physics-Informed Neural Networks for Fluid Mechanics

Abstract

Physics-informed machine learning is a novel approach to solving flow problems with physics-informed neural networks (PINNs), that combines physical knowledge and machine learning.
This study aims to investigate the potential of the application of PINNs in fluid mechanics problems by solving two practical flow problems.

The first case considers the reconstruction of the full, time accurate flow fields with PINNs from partial data in the wake of an airfoil with periodic vortex shedding.
The results have shown a decent success in flow reconstruction case, but has trouble maintaining a high accuracy at higher time values.
This is likely due to the lack of a mechanism forcing a time marching approach to prevent information flowing in the opposite direction of the positive time axis.

The second case attempts to train PINNs on a steady flow problems with parametric NACA airfoils first to devise a strategy for training PINNs on a parameteric airfoil and show its feasibility.
This is followed by using the found strategy to train PINNs for the more complex flow cases with PARSEC airfoils to use them as fast surrogate flow solvers, while still producing the full flow fields with a comparable accuracy to conventional CFD.

Overall, the flow fields inferred by the PINNs have shown a good qualitative match with the OpenFOAM validation data, even in the most complex case with a PARSEC airfoil, which makes them sufficiently accurate as a surrogate flow solver for a preliminary design optimization.
These results show not only the technical feasibility of PINNs for fluid mechanics, but also a practical value with accelerating the computation time up to a factor of 3.7 when accounting for the training time and producing the OpenFOAM training data.