An Artificial Neural Network based Solution Scheme to periodic Homogenization. Issue 1 (18th November 2019)

• Record Type: Journal Article
• Authors: Göküzüm, Felix Selim; Nguyen, Lu Trong Khiem; Keip, Marc-André
• Other Names: Eberhardsteiner J. guestEditor.; Schöberl M. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 19:Issue 1(2019)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2019-11-18
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201900271
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: Artificial neural networks (ANNs) have aroused research's and industry's interest due to their excellent approximation properties and are broadly used nowadays in the field of machine learning . In the present contribution, ANNs are used for finding solutions of periodic homogenization problems. The construction of ANN‐based trial functions that satisfy the given boundary conditions on the microscale allows for the unconstrained optimization of a global energy potential. Goal of the present approach is a memory efficient solution scheme as ANNs are known to fit complicated functions with a relatively small number of internal parameters. The method is tested for a three‐dimensional example using a global trial function and is qualitatively compared to a fast Fourier transform (FFT) based simulation.