Accounting for Hysteresis and Eddy Currents in Finite Element Simulations of Ferromagnetic Laminated Cores using a Recurrent Neural Network

2026-07-15

AI Summary

This study addresses the high computational cost of high-fidelity finite element simulation for laminated electromagnetic devices, which must simultaneously account for hysteresis and eddy current effects. The authors propose a general-purpose surrogate model based on a recurrent neural network (RNN), trained for the first time on diverse synthetic magnetic field sequences to jointly capture the coupled hysteresis–eddy current behavior. This RNN-based model is seamlessly embedded into a two-dimensional magnetic vector potential finite element framework. The approach achieves accuracy closely matching that of reference laminated models while incurring only approximately twice the computational overhead of simulations neglecting hysteresis—dramatically improving efficiency. The work also provides open-source, reusable standalone components to facilitate efficient engineering simulations.

Abstract

Incorporating hysteresis and eddy currents into finite element simulations of laminated-core electrical machines is computationally challenging. Resolving the fields inside the laminations at each integration point and at every nonlinear iteration leads to computational costs several orders of magnitude higher than anhysteretic simulations, making such approaches impractical for design applications. Conversely, simplified models accounting only for magnetic saturation are becoming increasingly inadequate as electrical machine topologies and operating conditions grow in complexity. In this context, machine learning surrogate modeling has emerged as a promising alternative, offering efficient and accurate approximations of complex electromagnetic behaviors. In this paper, a recurrent neural network is trained as a surrogate of a laminated-core material model for an isotropic laminated core, and is integrated into realistic two-dimensional magnetodynamic finite element simulations based on a magnetic vector potential formulation. The proposed approach achieves excellent agreement with the reference laminated-core model while limiting the computational cost to about twice that of an anhysteretic simulation. By training the recurrent neural network on a sufficiently diverse set of artificially generated magnetic field sequences designed to mimic those encountered in electrical machine simulations, the proposed approach can be readily applied across a wide range of finite element simulations. Furthermore, the trained surrogate model is provided as a standalone component that can be easily incorporated into existing computational frameworks. It is publicly available at https://gitlab.onelab.info/getdp/lamnet.

Problem

• hysteresis
• eddy currents
• finite element simulation
• laminated cores
• computational cost

Innovation

• Recurrent Neural Network
• Hysteresis Modeling
• Eddy Currents
• Finite Element Simulation
• Surrogate Modeling