Learning the solution operator of two-dimensional incompressible Navier-Stokes equations using physics-aware convolutional neural networks
This addresses the need for geometry-agnostic models in fluid dynamics simulations, reducing retraining efforts for new geometries, though it appears incremental as it builds on existing physics-aware ML and U-Net architectures.
The paper tackles the problem of learning solution operators for the 2D incompressible Navier-Stokes equations across varying geometries without parametrization, using a physics-aware convolutional neural network combined with finite difference methods, and shows results compared to a state-of-the-art data-based approach.
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.