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.

翻译：近年来，将物理引入机器学习的概念已变得广泛流行。然而，大多数包含物理信息的机器学习技术仍局限于单一几何形状或一组可参数化的几何形状。因此，即使几何形状仅有微小修改，仍需要针对新几何形状重新训练模型。本研究提出一种无需参数化即可学习变几何条件下稳态纳维-斯托克斯方程近似解的技术。该技术基于类U-Net的卷积神经网络与有限差分法领域成熟的离散化方法的结合。我们将物理感知CNN的结果与最先进的基于数据的方法进行了比较。此外，还展示了该方法与基于数据的方法结合时的表现。