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Convolutional neural networks (CNN) have shown great potentials and have been proven to be an effective tool for some image-based deep learning tasks in the field of computational electromagnetism (CEM). In this work, an energy-based physics-informed neural network (EPINN) is proposed for low-frequency electromagnetic computation. Two different physics-informed loss functions are designed. To help the network focus on the region of interest instead of computing the whole domain on average, the magnetic energy norm error loss function is proposed. Besides, the methodology of energy minimization is integrated into the CNN by introducing the magnetic energy error loss function. It is observed that the introduction of the physics-informed loss functions improved the accuracy of the network with the same architecture and database. Meanwhile, these changes also cause the network to be more sensitive to some hyperparameters and makes the training process oscillate or even diverge. To address this issue, the sensitivity of the network hyperparameters for both physics-informed loss functions are further investigated. Numerical experiments demonstrate that the proposed approaches have good accuracy and efficiency with fine-tuned hyperparameters. Furthermore, the post-test illustrates that the EPINN has excellent interpolation performance and can obtain good extrapolation results under certain restrictions.

A numerical issue arises when we extend the convolutional neural network (CNN) U-net to the anisotropic magnetostatic field computation. The output magnetic field has a significant gradient with respect to the input geometry parameter, which introduces inevitable errors in the training process to degrade the performance of deep learning (DL). To address this issue, the subset selection approach is utilized to divide the whole database into serval subsets, where the samples are assigned according to the gradient between the input and output. Then these subsets with different sample densities are combined into a global one. Taking the uniform dataset with the same sample size as a comparison, the influence of subset selection on DL is investigated by comparing the performance of CNN on different datasets. Numerical experiments illustrate that the adaptive subset selection can be employed to improve the accuracy and efficiency of the CNN network.

Deep learning (DL) has attracted more and more attention in computational electromagnetism. Particularly, the Convolutional Neural Network (CNN) is one of the most popular learning models in DL due to its excellent capacity for feature extraction and convergence. The efficiency of CNN mainly depends on how many training samples are needed to effectively converge the network. The sample preparation process often involves a lot of numerical computations, which can be very expensive and time-consuming. In this paper, based on the traditional DL network training procedure, two different approaches, namely adding smart training samples and reference samples, are proposed to help the DL network converge. The smart sample selection is based on a greedy algorithm, which can be applied for both training and reference samples. The influences of these two approaches on the CNN training process are investigated by an example of the coupled magneto-thermal computation applied to a transformer. Numerical results show that the two proposed approaches can significantly help the network to converge and improve the efficiency of the DL model.

This paper aims to investigate the approach combine the deep learning (DL) and finite element method for the magneto-thermal coupled problem.

In this paper, a comparison between the model order reduction technique and deep learning technique is proposed, from the aspect of the surrogate model construction in computational electromagnetism. The merit and demerit of both approaches are discussed and compared via an academic application of magneto-thermal coupled analysis.

In this paper, a surrogate model base on deep learning (DL) is proposed to predict the hysteresis loops of ferro-magnetic materials. The databases of hysteresis loops were measured on the MPG200D Brockhaus equipment with an Epsteinframe. In order to reduce the experimental cost and accelerate measurements, a surrogate model based on the convolutional neural network (CNN) is proposed. First, presenting the measurement results in the form of 256× 256 × 1 images and extract the 6 most characteristic parameters, namely peak magnetic flux density, frequency, maximum magnetic field strength, remanence, coercivity, and the area of the hysteresis loop. All these physical parameters are taken as the label in the supervised DL process. These labe linformation are normalized to form a Gaussian distribution image of 256× 256 × 3 as the input, and the corresponding B-H curve is the output. Using image-to-image CNN U-net, once the network is effectively trained, the hysteresis loops under other excitation parameters can be predicted without further measurement. Our numerical examples show that the prediction results agree well with the measurement results. The sensitivity of CNN for hysteresis loops prediction with respect to the hyperparameters are investagted. A set of empirical hyperparameter configurations isput forward to guarantee an efficient convergence. This research shows that the proposed approach can be an efficient tool to predict the hysteresis loop of ferromagnetic materials under different circumstances, which can potentially contribute to nonlinear hysteresis FEM computation.