Topology optimization in magnetic shield design by using density method in combination with CNN

Rie Isshiki*, Ryota Kawamata, Shinji Wakao, Noboru Murata

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Purpose: The density method is one of the powerful topology optimization methods of magnetic devices. The density method has the advantage that it has a high degree of freedom of shape expression which results in a high-performance design. On the other hand, it has also the drawback that unsuitable shapes for actually manufacturing are likely to be generated, e.g. checkerboards or grayscale. The purpose of this paper is to develop a method that enables topology optimization suitable for fabrication while taking advantage of the density method. Design/methodology/approach: This study proposes a novel topology optimization method that combines convolutional neural network (CNN) as an effective smoothing filter with the density method and apply the method to the shield design with magnetic nonlinearity. Findings: This study demonstrated some numerical examples verifying that the proposed method enables to efficiently obtain a smooth and easy-to-manufacture shield shape with high shielding ability. A network architecture suitable as smoothing filter was also exemplified. Originality/value: In the field of magnetic field analysis, very few studies have verified the usefulness of smoothing by using CNN in the topology optimization of magnetic devices. This paper develops a novel topology optimization method that skillfully combines CNN with the nonlinear magnetic field analysis and also clarifies a suitable network architecture that makes it possible to obtain a target device shape that is easy to manufacture while minimizing the objective function value.


  • Convolutional neural network
  • Deep image prior
  • Density method
  • Finite element method
  • Magnetic nonlinearity
  • Magnetic shield
  • Magnetic shielding
  • Topology optimization

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Theory and Mathematics
  • Applied Mathematics
  • Electrical and Electronic Engineering


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