Universität zu Köln

Heinlein, Alexander, Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin and Weber, Janine (2018). Machine Learning in Adaptive FETI-DP - A Comparison of Smart and Random Training Data. Technical Report.

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Abstract

Adaptive FETI-DP (Finite Element Tearing and Interconnecting - Dual-Primal) methods are considered for the solution of two-dimensional scalar elliptic model problems with complex coefficient distributions where large coefficient jumps can occur along or across the domain decomposition interface. The adaptive coarse space is obtained by solving certain generalized eigenvalue problems on subdomain edges. In order to reduce the number of eigenvalue problems, a machine learning based strategy using a neural network to predict the geometric location of critical edges can be applied in a preprocessing step. Here, the effect of different types of training data sets on the robustness of the machine learning adaptive FETI-DP algorithm is investigated. Therefore, the neural network is first trained on different data sets and then the machine learning model is evaluated for a coefficient distribution obtained from a realistic dual-phase steel microstructure. It can be observed that the best results are obtained using a priori knowledge (smart data), whereas purely random data yields bad results. However, by imposing some structure on the random data and increasing the size of the data set, the performance is comparable to the smart data.

Item Type:	Preprints, Working Papers or Reports (Technical Report)
Creators:	Creators Email ORCID ORCID Put Code Heinlein, Alexander alexander.heinlein@uni-koeln.de UNSPECIFIED UNSPECIFIED Klawonn, Axel axel.klawonn@uni-koeln.de orcid.org/0000-0003-4765-7387 UNSPECIFIED Lanser, Martin martin.lanser@uni-koeln.de UNSPECIFIED UNSPECIFIED Weber, Janine janine.weber@uni-koeln.de UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-90164
Series Name at the University of Cologne:	Technical report series. Center for Data and Simulation Science
Volume:	2018,7
Date:	16 November 2018
Language:	English
Faculty:	Central Institutions / Interdisciplinary Research Centers
Divisions:	Weitere Institute, Arbeits- und Forschungsgruppen > Center for Data and Simulation Science (CDS)
Subjects:	Data processing Computer science Mathematics Technology (Applied sciences)
Uncontrolled Keywords:	Keywords Language Adaptive FETI-DP English Machine Learning English
URI:	http://kups.ub.uni-koeln.de/id/eprint/9016