2023/08/04 by Viktor Grimm, Grimm, Viktor, Alexander Heinlein +3 · 1 citation
Computer Science · Engineering · Physics and Astronomy · #35Q30 #65N22 #68T07 #68T10 #Computational Engineering #Computational Physics and Python Applications #FOS: Computer and information sciences #FOS: Mathematics #Finance #Fluid Dynamics and Vibration Analysis #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #and Science (cs.CE)
paper · pdf · doi:10.48550/arxiv.2308.02137
openalex publication_date 2023/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.