Universität zu Köln

Grimm, Viktor ORCID: 0000-0001-5300-3705, Heinlein, Alexander ORCID: 0000-0003-1578-8104 and Klawonn, Axel ORCID: 0000-0003-4765-7387 (2025). Learning the solution operator of two-dimensional incompressible Navier-Stokes equations using physics-aware convolutional neural networks. Journal of Computational Physics, 535. pp. 1-25. Elsevier. ISSN 0021-9991

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Abstract

[Artikel-Nr.: 114027] 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.

Item Type:	Article
Creators:	Creators Email ORCID ORCID Put Code Grimm, Viktor UNSPECIFIED https://orcid.org/0000-0001-5300-3705 UNSPECIFIED Heinlein, Alexander UNSPECIFIED https://orcid.org/0000-0003-1578-8104 UNSPECIFIED Klawonn, Axel UNSPECIFIED https://orcid.org/0000-0003-4765-7387 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-804502
Identification Number:	10.1016/j.jcp.2025.114027
Journal or Publication Title:	Journal of Computational Physics
Volume:	535
Page Range:	pp. 1-25
Number of Pages:	25
Date:	23 August 2025
Publisher:	Elsevier
ISSN:	0021-9991
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute Weitere Institute, Arbeits- und Forschungsgruppen > Center for Data and Simulation Science (CDS)
Subjects:	Data processing Computer science Mathematics
Uncontrolled Keywords:	Keywords Language Convolutional neural networks ; Computational fluid dynamics ; Machine learning ; Scientific machine learning English
['eprint_fieldname_oa_funders' not defined]:	Publikationsfonds UzK
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/80450