Machine learning aided multiscale magnetostatics

Fadi Aldakheel*, Celal Soyarslan, Hari Subramani Palanisamy, Elsayed Saber Elsayed

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

5 Citations (Scopus)
8 Downloads (Pure)


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.

Original languageEnglish
Article number104726
Number of pages14
JournalMechanics of materials
Early online date30 Jun 2023
Publication statusPublished - Sept 2023


  • Convolutional Neural Network (CNN)
  • Homogenization
  • Magnetostatics
  • 2023 OA procedure


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