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Constrained neural network training and its application to hyperelastic material modeling

Weber, P. 1; Geiger, J. 1; Wagner, W. 1
1 Institut für Baustatik (IBS), Karlsruher Institut für Technologie (KIT)


Neural networks (NN) have been studied and used widely in the field of computational mechanics, especially to approximate material behavior. One of their disadvantages is the large amount of data needed for the training process. In this paper, a new approach to enhance NN training with physical knowledge using constraint optimization techniques is presented. Specific constraints for hyperelastic materials are introduced, which include energy conservation, normalization and material symmetries. We show, that the introduced enhancements lead to better learning behavior with respect to well known issues like a small number of training samples or noisy data. The NN is used as a material law within a finite element analysis and its convergence behavior is discussed with regard to the newly introduced training enhancements. The feasibility of NNs trained with physical constraints is shown for data based on real world experiments. We show, that the enhanced training outperforms state-of-the-art techniques with respect to stability and convergence behavior within FE simulations.

Verlagsausgabe §
DOI: 10.5445/IR/1000137004
Veröffentlicht am 31.08.2021
DOI: 10.1007/s00466-021-02064-8
Zitationen: 16
Web of Science
Zitationen: 14
Zitationen: 19
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Baustatik (IBS)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2021
Sprache Englisch
Identifikator ISSN: 0178-7675, 1432-0924
KITopen-ID: 1000137004
Erschienen in Computational Mechanics
Verlag Springer
Band 68
Seiten 1179–1204
Vorab online veröffentlicht am 03.08.2021
Schlagwörter Neural networks, Material modeling, Constrained optimization, Regularization, Hyperelasticity, FEM, Shell structures
Nachgewiesen in Dimensions
Web of Science
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