Efficient modelling of permanent magnet field distribution for deep learning applications

• We represented the axial, azimuthal and radial components of the magnetic field created by permanent magnets and uniform magnetisations in semi-analytical expressions (SAE). • We built a machine learning model using the training data generated by the SAE. • The machine learning model can predict the field distributions of permanent magnets in various configurations. • The predicted magnetic field using the machine learning model is in good agreement with the ground-truth. • The machine learning model is much faster than the SAE and Finite element method in terms of computational time. Permanent magnets are essential components in a range of applications from robotics to energy harvesting devices. Computing the field distribution of permanent magnets is crucial for designing and optimising these devices, but currently existing techniques, such as the Finite Element Method (FEM), are very time-consuming. Deep learning (DL) has been widely utilised to solve regression and classification problems and could enable an efficient computation of permanent magnet field distributions. However, deep learning requires large amounts of training data, which is difficult to obtain with current methods. In this work we represented the axial, azimuthal and radial components of the magnetic field created by permanent magnets and uniform magnetisations in semi-analytical expressions (SAE). These forms can be further simplified, and we validated these against the FEM for individual geometries such as an elliptical cylinder and a cone. The computational efficiency of the semi-analytical forms enables the generation of training datasets. Finally, we built a machine learning model using the training data generated by the SAEs and demonstrate that the machine learning model can predict the field distributions of permanent magnets in various configurations. The predicted magnetic field using the machine learning model is in good agreement with the ground-truth, with r 2 for the axial, azimuthal and radial components being 0.999, 0.997 and 0.998, respectively for the magnetised elliptical cylinders, and 0.999, 0.999, 0.998 for the magnetised cones. Furthermore, the computational times of the machine learning models when executed on a CPU are more than 28 and 12 times faster than the SAEs of the elliptical cylinders and cones, respectively; the models are very fast to execute on a GPU with 22.7 s for the elliptical cylinders and 36.8 s for the cones. This work shows that it is possible to train a machine learning model to predict permanent magnet field distributions based on a training with semi-analytical expressions of various magnet geometries. The code for generating the training data, constructing the machine learning model and applying the model to new data is made openly available ( https://github.com/vantainguyen/MagField_DataGen_Deep-learning ).