Learning the solution operator of two-dimensional incompressible Navier-Stokes equations using physics-aware convolutional neural networks

• URL: http://arxiv.org/abs/2308.02137v1
• Date: Fri, 4 Aug 2023 05:09:06 GMT
• Title: Learning the solution operator of two-dimensional incompressible Navier-Stokes equations using physics-aware convolutional neural networks
• Authors: Viktor Grimm, Alexander Heinlein, Axel Klawonn
• Abstract summary: 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. The results of our physics-aware CNN are compared to a state-of-the-art data-based approach.
• Score: 68.8204255655161
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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