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.

通过结合U-Net-like CNN和有限差分法领域的已建立的离散化方法，我们介绍了一种在不同几何形状中学习稳态Navier-Stokes方程近似解的技术，无需参数化。我们将基于物理的CNN的结果与基于数据的方法进行了比较，并展示了将我们的方法与基于数据的方法相结合的性能。

利用物理感知卷积神经网络学习二维不可压缩纳维-斯托克斯方程的解算器