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Evaluating magnetic fields using deep learning

Mohammad Mushfiqur Rahman (Computational Electromagnetics Lab, McGill University, Montreal, Canada)
Arbaaz Khan (Computational Electromagnetics Lab, McGill University, Montreal, Canada)
David Lowther (Computational Electromagnetics Lab, McGill University, Montreal, Canada)
Dennis Giannacopoulos (Computational Electromagnetics Lab, McGill University, Montreal, Canada)

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering

ISSN: 0332-1649

Article publication date: 11 August 2023

Issue publication date: 21 November 2023




The purpose of this paper is to develop surrogate models, using deep learning (DL), that can facilitate the application of EM analysis software. In the current status quo, electrical systems can be found in an ever-increasing range of products that are part of everyone’s daily live. With the advances in technology, industries such as the automotive, communications and medical devices have been disrupted with new electrical and electronic systems. The innovation and development of such systems with increasing complexity over time has been supported by the increased use of electromagnetic (EM) analysis software. Such software enables engineers to virtually design, analyze and optimize EM systems without the need for building physical prototypes, thus helping to shorten the development cycles and consequently cut costs.


The industry standard for simulating EM problems is using either the finite difference method or the finite element method (FEM). Optimization of the design process using such methods requires significant computational resources and time. With the emergence of artificial intelligence, along with specialized tools for automatic differentiation, the use of DL has become computationally much more efficient and cheaper. These advances in machine learning have ushered in a new era in EM simulations where engineers can compute results much faster while maintaining a certain level of accuracy.


This paper proposed two different models that can compute the magnetic field distribution in EM systems. The first model is based on a recurrent neural network, which is trained through a data-driven supervised learning method. The second model is an extension to the first with the incorporation of additional physics-based information to the authors’ model. Such a DL model, which is constrained by the laws of physics, is known as a physics-informed neural network. The solutions when compared with the ground truth, computed using FEM, show promising accuracy for the authors’ DL models while reducing the computation time and resources required, as compared to previous implementations in the literature.


The paper proposes a neural network architecture and is trained with two different learning methodologies, namely, supervised and physics-based. The working of the network along with the different learning methodologies is validated over several EM problems with varying levels of complexity. Furthermore, a comparative study is performed regarding performance accuracy and computational cost to establish the efficacy of different architectures and learning methodologies.



Rahman, M.M., Khan, A., Lowther, D. and Giannacopoulos, D. (2023), "Evaluating magnetic fields using deep learning", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 42 No. 5, pp. 1115-1132.



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