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An Artificial Neural Network based Solution Scheme to periodic Homogenization
Author(s) -
Göküzüm Felix Selim,
Nguyen Lu Trong Khiem,
Keip Marc-André
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900271
Subject(s) - artificial neural network , homogenization (climate) , microscale chemistry , fast fourier transform , computer science , scheme (mathematics) , fourier transform , boundary value problem , mathematical optimization , artificial intelligence , mathematics , algorithm , mathematical analysis , biodiversity , ecology , mathematics education , biology
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.