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:
CreatorsEmailORCID
Heinlein, Alexanderalexander.heinlein@uni-koeln.deUNSPECIFIED
Klawonn, Axelaxel.klawonn@uni-koeln.deorcid.org/0000-0003-4765-7387
Lanser, Martinmartin.lanser@uni-koeln.deUNSPECIFIED
Weber, Janinejanine.weber@uni-koeln.deUNSPECIFIED
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
Subjects: Data processing Computer science
Mathematics
Technology (Applied sciences)
Uncontrolled Keywords:
KeywordsLanguage
Adaptive FETI-DPEnglish
Machine LearningEnglish
Faculty: Central Institutions / Interdisciplinary Research Centers
Divisions: Central Institutions / Interdisciplinary Research Centers > Center for Data and Simulation Science
Language: English
Date: 16 November 2018
URI: http://kups.ub.uni-koeln.de/id/eprint/9016

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