Deep Learning for Magnetic Field Estimation

This paper investigates the feasibility of novel data-driven deep learning (DL) models to predict the solution of Maxwell’s equations for low-frequency electromagnetic (EM) devices. With ground truth (empirical evidence) data being generated from a finite-element analysis solver, a deep convolutional neural network is trained in a supervised manner to learn a mapping for magnetic field distribution for topologies of different complexities of geometry, material, and excitation, including a simple coil, a transformer, and a permanent magnet motor. Preliminary experiments show DL model predictions in close agreement with the ground truth. A probabilistic model is introduced to improve the accuracy and to quantify the uncertainty in the prediction, based on Monte Carlo dropout. This paper establishes a basis for a fast and generalizable data-driven model used in the analysis, design, and optimization of EM devices.

[1]  Geoffrey E. Hinton,et al.  ImageNet classification with deep convolutional neural networks , 2012, Commun. ACM.

[2]  P.T. Krein,et al.  Capabilities of finite element analysis and magnetic equivalent circuits for electrical machine analysis and design , 2008, 2008 IEEE Power Electronics Specialists Conference.

[3]  Zoubin Ghahramani,et al.  Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning , 2015, ICML.

[4]  Nitish Srivastava,et al.  Dropout: a simple way to prevent neural networks from overfitting , 2014, J. Mach. Learn. Res..

[5]  Roberto Cipolla,et al.  Bayesian SegNet: Model Uncertainty in Deep Convolutional Encoder-Decoder Architectures for Scene Understanding , 2015, BMVC.

[6]  Ji Wu,et al.  Study on a Poisson's equation solver based on deep learning technique , 2017, 2017 IEEE Electrical Design of Advanced Packaging and Systems Symposium (EDAPS).

[7]  Vahid Ghorbanian,et al.  A Statistical Solution to Efficiently Optimize the Design of an Inverter-Fed Permanent-Magnet Motor , 2017, IEEE Transactions on Industry Applications.

[8]  Francesco Visin,et al.  A guide to convolution arithmetic for deep learning , 2016, ArXiv.

[9]  Ken Perlin,et al.  Accelerating Eulerian Fluid Simulation With Convolutional Networks , 2016, ICML.

[10]  Vahid Ghorbanian,et al.  A Computer-Aided Design Process for Optimizing the Size of Inverter-Fed Permanent Magnet Motors , 2018, IEEE Transactions on Industrial Electronics.

[11]  Roberto Cipolla,et al.  SegNet: A Deep Convolutional Encoder-Decoder Architecture for Robust Semantic Pixel-Wise Labelling , 2015, CVPR 2015.