TY - JOUR

T1 - Machine learning aided multiscale magnetostatics

AU - Aldakheel, Fadi

AU - Soyarslan, Celal

AU - Palanisamy, Hari Subramani

AU - Elsayed, Elsayed Saber

N1 - Funding Information: Fadi Aldakheel (FA) gratefully acknowledges support for this research by the “German Research Foundation” (DFG) in the International Research Training Group (IRTG) 2657 program (Grant Reference Number 433082294 ).

PY - 2023/9

Y1 - 2023/9

N2 - Computational material modeling using advanced numerical techniques speeds up the design process and reduces the costs of developing new engineering products. In the field of multiscale modeling, huge computation efforts are expected for modeling heterogeneous materials while trying to reach high accuracy levels. In this work, a machine learning approach, namely the convolutional neural network (CNN), is developed as a solution providing a high level of accuracy while being computationally efficient. The input for the CNN model consists of two/three-dimensional images of artificial periodic and biphasic microstructures in the form of nonoverlapping and overlapping, mono- and polydisperse circular/spherical inclusion systems, which are generated by a random sequential inhibition process. These correspond to Statistical Volume Elements (SVE). Considering linear magnetostatics at the microscale, the output is the apparent permeability of the SVE. Training and testing data for the apparent properties is produced with finite element method-based two-scale asymptotic homogenization. The model efficiency is revealed by employing some representative examples in two and three-dimensional settings. In this regard, the performance of the CNN model is assessed with the applied computational homogenization method relating to the accuracy and computational efficiency. The results with the CNN model show high accuracy in predicting the homogenized permeability and a significant decrease in computation time.

AB - Computational material modeling using advanced numerical techniques speeds up the design process and reduces the costs of developing new engineering products. In the field of multiscale modeling, huge computation efforts are expected for modeling heterogeneous materials while trying to reach high accuracy levels. In this work, a machine learning approach, namely the convolutional neural network (CNN), is developed as a solution providing a high level of accuracy while being computationally efficient. The input for the CNN model consists of two/three-dimensional images of artificial periodic and biphasic microstructures in the form of nonoverlapping and overlapping, mono- and polydisperse circular/spherical inclusion systems, which are generated by a random sequential inhibition process. These correspond to Statistical Volume Elements (SVE). Considering linear magnetostatics at the microscale, the output is the apparent permeability of the SVE. Training and testing data for the apparent properties is produced with finite element method-based two-scale asymptotic homogenization. The model efficiency is revealed by employing some representative examples in two and three-dimensional settings. In this regard, the performance of the CNN model is assessed with the applied computational homogenization method relating to the accuracy and computational efficiency. The results with the CNN model show high accuracy in predicting the homogenized permeability and a significant decrease in computation time.

KW - Convolutional Neural Network (CNN)

KW - Homogenization

KW - Magnetostatics

UR - http://www.scopus.com/inward/record.url?scp=85166626338&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2301.12782

DO - 10.48550/arXiv.2301.12782

M3 - Article

AN - SCOPUS:85166626338

VL - 184

JO - Mechanics of materials

JF - Mechanics of materials

SN - 0167-6636

M1 - 104726

ER -