Universität zu Köln

Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin ORCID: 0000-0002-4232-9395 and Weber, Janine ORCID: 0000-0002-6692-2230 (2024). Machine learning and domain decomposition methods - a survey. Computational Science and Engineering, 1 (1). pp. 1-31. Springer Nature. ISSN 2948-1597

PDF s44207-024-00003-y..pdf Download (2MB)

Abstract

[Artikel-Nr.: 2] Hybrid algorithms, which combine black-box machine learning methods with experience from traditional numerical methods and domain expertise from diverse application areas, are progressively gaining importance in scientific machine learning and various industrial domains, especially in computational science and engineering. In the present survey, several promising avenues of research will be examined which focus on the combination of machine learning (ML) and domain decomposition methods (DDMs). The aim of this survey is to provide an overview of existing work within this field and to structure it into domain decomposition for machine learning and machine learning-enhanced domain decomposition, including: domain decomposition for classical machine learning, domain decomposition to accelerate the training of physics-aware neural networks, machine learning to enhance the convergence properties or computational efficiency of DDMs, and machine learning as a discretization method in a DDM for the solution of PDEs. In each of these fields, we summarize existing work and key advances within a common framework and, finally, discuss ongoing challenges and opportunities for future research.

Item Type:	Article
Creators:	Creators Email ORCID ORCID Put Code Klawonn, Axel UNSPECIFIED https://orcid.org/0000-0003-4765-7387 UNSPECIFIED Lanser, Martin UNSPECIFIED https://orcid.org/0000-0002-4232-9395 UNSPECIFIED Weber, Janine UNSPECIFIED https://orcid.org/0000-0002-6692-2230 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-814839
Identification Number:	10.1007/s44207-024-00003-y
Journal or Publication Title:	Computational Science and Engineering
Volume:	1
Number:	1
Page Range:	pp. 1-31
Number of Pages:	31
Date:	23 September 2024
Publisher:	Springer Nature
ISSN:	2948-1597
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Center for Data and Simulation Science
Subjects:	Data processing Computer science Mathematics
['eprint_fieldname_oa_funders' not defined]:	Publikationsfonds UzK
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/81483