Learning the solution operator of two-dimensional incompressible
  Navier-Stokes equations using physics-aware convolutional neural networks
Viktor Grimm Alexander Heinlein Axel Klawonn
In recent years, the concept of introducing physics to machine learning has
become widely popular. Most physics-inclusive ML-techniques however are still
limited to a single geometry or a set of parametrizable geometries. Thus, there
remains the need to train a new model for a new geometry, even if it is only
slightly modified. With this work we introduce a technique with which it is
possible to learn approximate solutions to the steady-state Navier--Stokes
equations in varying geometries without the need of parametrization. This
technique is based on a combination of a U-Net-like CNN and well established
discretization methods from the field of the finite difference method.The
results of our physics-aware CNN are compared to a state-of-the-art data-based
approach. Additionally, it is also shown how our approach performs when
combined with the data-based approach.