Introduction
For more than four decades, Finite Element Method (FEM) simulation has been the foundational tool used to design motors, transformers, inductors, actuators, magnetic bearings, superconducting magnets, and countless electromagnetic devices. Engineers have relied on FEM to predict magnetic field distributions, forces, losses, temperature effects, and dynamic performance with high precision. Yet despite its maturity, traditional electromagnetic FEM still suffers from fundamental limitations. Nonlinear materials, eddy currents, hysteresis, multi-physics couplings, and 3D transient problems often push classical solvers to their limits. As devices grow more complex and design cycles accelerate, even the most advanced commercial tools cannot always meet the demands of industry and research.
Artificial intelligence (AI) is now transforming this landscape. Machine learning (ML), physics-informed neural networks (PINNs), and hybrid numerical–AI approaches are emerging as powerful accelerators for FEM-based electromagnetic analysis. Instead of relying solely on mesh refinement, iterative solvers, and brute-force optimization, engineers can integrate AI models trained on field data to predict electromagnetic behavior thousands of times faster than conventional solvers.
AI is not replacing FEM. Instead, AI is enabling a new era of hybrid simulation, where FEM continues to deliver high-fidelity physics while AI provides speed, generalization, and predictive efficiency. Together, they form a foundation for faster design, real-time simulation, and previously impossible optimization workflows.
Limitations of Traditional Electromagnetic FEM
While the FEM is noted for its high accuracy, it encounters three principal bottlenecks that advancements in artificial intelligence may help address. First, the modeling of materials such as magnetic steels, magnetic alloys, ferrites, rare-earth magnets, and amorphous alloys presents nonlinear B–H relationships. Iterative solvers must continuously adjust permeability, pursue convergence, and monitor local saturation levels. During each nonlinear iteration, it is necessary to reassemble or reevaluate the system matrix, greatly increasing computational requirements.
Second, contemporary electromagnetic devices rarely consist solely of magnetic components. Comprehensive simulation typically requires integrated analysis of heat transfer (including losses and cooling), mechanical deformation and magnetostriction, superconducting quench phenomena, acoustic noise, and fluid dynamics within cooling channels. These multifaceted interactions compound the computational complexity and substantially extend solver runtimes.
Finally, optimization of magnetic devices involves considerations such as torque density, acoustic performance, thermal constraints, flux ripple, minimization of rare-earth magnet usage, and operational efficiency across varying load cycles. Each additional optimization criterion necessitates further FEM evaluations; realistic optimization approaches may demand hundreds or thousands of runs, rendering brute-force methods inefficient. These persistent challenges highlight the potential for AI-driven computational enhancements.
AI-Driven Surrogate Models for Electromagnetic FEM
One of the earliest and most impactful applications of artificial intelligence in the field of electromagnetics is the development of surrogate models. These models are built using neural networks to closely approximate the relationship between the typical inputs used in FEM simulations—such as device geometry, applied currents, and material properties—and the resulting outputs, including electromagnetic fields, flux linkage, torque, force, and inductance.
After the surrogate models are trained on relevant data, they deliver several important advantages. First, they can make predictions almost instantaneously, often within microseconds. This rapid evaluation produces smooth response surfaces, which are essential for design optimization and sensitivity analysis. Additionally, the use of surrogate models eliminates the need for repeated meshing of the geometry, a process that is often time-consuming in conventional FEM workflows. Because the surrogate models are compatible with various optimization algorithms, they allow engineers to explore design spaces thousands of times faster than would be possible using traditional methods.
Research in areas such as superconducting magnet design and plasma confinement systems has demonstrated that replacing repeated FEM simulations with neural network surrogates yields speed improvements ranging from 100× to 1000×. This substantial acceleration fundamentally changes the simulation workflow. Initially, FEM is used only to generate training data for the surrogate models. Once trained, the AI-driven models take over the design exploration phase, rapidly evaluating potential configurations. The FEM solver is then used again only in the final stages, where it validates the most promising designs.
This synergistic approach, where FEM and AI complement each other, leads to significantly shorter development cycles and enables new opportunities for design and optimization in electromagnetic systems.
AI-Based Constitutive Models for Magnetic Materials
Electromagnetic FEM’s nonlinear material models are computationally intensive, requiring repeated evaluation of B–H curve interpolation, permeability updates, hysteresis modeling, frequency-based losses, and minor loops. AI-trained models offer a solution by instantly providing magnetization, permeability, and dynamic hysteresis data—eliminating iterative inversion or lookups. Key benefits include a 50–70% cut in solver iterations, smoother convergence, easy embedding of temperature or stress effects, and simplified dynamic hysteresis modeling. These AI approaches integrate directly with standard FEM solvers.
Physics-Informed Neural Networks (PINNs):
Toward Mesh-Free Electromagnetics
Physics-Informed Neural Networks (PINNs) integrate Maxwell’s equations directly into neural networks, enabling solutions that automatically satisfy Gauss’s laws, Ampere’s law, Ohm’s law, and constitutive relations. This approach minimizes or eliminates the need for meshing, stiffness matrices, time-stepping, and boundary elements. Though still in early stages, PINNs show strong potential in magnetostatics, low-frequency fields, eddy-current shielding, transformer core modeling, and nonlinear 2D domains. Ultimately, PINNs could partially replace FEM workflows or function as hybrid modules within commercial solvers.
The Role of AI in Electromagnetic Transient FEM Analysis
The most computationally demanding area of electromagnetic analysis is three-dimensional transient finite element modeling (FEM), especially under conditions where eddy currents dominate, skin depth is extremely small, materials exhibit nonlinear hysteresis, switching frequencies are high, or when multi-physics couplings are present. These scenarios necessitate extremely fine mesh densities near conductive surfaces and tiny time steps to maintain numerical stability. Such requirements can result in simulations with millions of degrees of freedom, often demanding the use of supercomputers or large GPU clusters. Artificial intelligence (AI) holds the promise of revolutionizing this field by fundamentally improving efficiency and computational speed.
Neural Models for Skin Depth and Eddy Currents
Skin depth (δ) in magnetic materials can shrink dramatically, reaching millimeters at 60 Hz, hundreds of microns at kilohertz frequencies, and tens of microns in magnetic steels with high permeability. Accurately resolving these thin layers with traditional FEM necessitates the use of extremely fine meshes, greatly increasing computational cost. AI provides an alternative approach: neural networks can be trained to learn the current penetration and diffusion behavior based on excitation frequency, material state, and nonlinear B–H characteristics. Instead of densely meshing the skin-depth regions, the solver can use a coarse mesh along with an AI-derived surface impedance or equivalent eddy-current model. This method can reduce computation time by a factor of 10 to 50 in three-dimensional systems.
AI-Accelerated Reduced-Order Models (ROMs)
Transient electromagnetic problems require FEM solvers to repeatedly compute phenomena such as field diffusion, flux variation, eddy-current loops, and saturation effects. AI-enhanced reduced-order models (ROMs) can efficiently approximate the time evolution of electromagnetic fields between FEM checkpoints. The typical workflow involves running a few “anchor” FEM time steps, using a neural ROM to predict intermediate time steps, and periodically correcting any drift with full FEM solves. This hybrid approach preserves physical accuracy while reducing runtime by 90–95% for extended simulations.
Neural Predictors for Adaptive Time-Stepping
Fast switching events in transient simulations require small time steps to avoid instability, while calm periods can tolerate larger time steps without loss of accuracy. AI models can forecast how rapidly electromagnetic fields will change, enabling adaptive time-stepping that automatically shrinks the time step during saturation or switching and expands it during slower evolution. This approach increases computational speed by 30–70% while maintaining numerical stability throughout the simulation.
The PINNs as Partial Replacements for Transient FEM
The PINNs have the capability to directly solve diffusion equations within conductive regions in the time domain. PINNs are particularly well-suited for smooth, frequency-based, or diffusion-dominated regions such as shields, conductive plates, and secondary structures in motors and transformers. In this hybrid simulation concept, the FEM solver manages geometry and strong nonlinearities, while the PINN addresses diffusion. This approach may define the future of transient electromagnetic simulation by combining the strengths of both methods.
AI for Inverse Electromagnetic Design
AI shifts design from simulation to direct generation, using neural networks to determine optimal geometries for desired fields. Key applications are in loudspeaker circuits, motors with higher torque, MRI gradient shapers, rare-earth magnet reduction, inductors, transformers, and magnetic levitation systems. This approach transforms FEM into data creation and positions AI as the driver of innovation.
The Hybrid FEM–AI Solver of the Future
Future electromagnetic solvers will integrate the finite element method (FEM) to ensure accurate physical modeling with artificial intelligence for enhanced speed, predictive capabilities, and optimization. Key advancements will encompass AI-driven meshing, neural material modeling, PINN–FEM hybrid solvers, instant surrogate models for optimization, automated topology generation, and real-time simulation tailored for control applications. These innovations will enable engineers to simulate and optimize magnetic systems within seconds rather than hours.
Conclusion
Electromagnetic FEM is entering the most important evolution in its history. AI is not replacing FEM—it is expanding it, accelerating it, and enabling entirely new workflows. By combining high-fidelity physics with the predictive power of AI, engineers can overcome traditional limitations, achieve faster convergence, model 3D transient effects without supercomputers, and explore vast design spaces in real time.
Future electromagnetic devices—motors, inductors, transformers, actuators, superconducting coils—will be designed with hybrid simulation tools where AI and FEM work together seamlessly. The engineers who master both technologies will lead the next era of innovation in electromagnetics.
References
[1] A. Khan and D. A. Lowther, "Physics Informed Neural Networks for Electromagnetic Analysis,"IEEE Trans. Magnetics, vol. 58, no. 9, pp. 1-4, Sept. 2022.
[2] M. Baldan, P. Di Barba and D. A. Lowther, "Physics-Informed Neural Networks for Inverse Electromagnetic Problems," IEEE Trans. Magnetics, vol. 59, no. 5, pp. 1-5, May 2023.
[3] Wan, Bingkuan, Gang Lei, Youguang Guo, and Jianguo Zhu. 2025. “Physics-Informed Neural Networks Based on Unsupervised Learning for Multidomain Electromagnetic Analysis.” IET Electric Power Applications: e70083. https://doi.org/10.1049/elp2.70083.
[4] H. Zhang, S. Li, T. Zhao, J. Song, and Z. Deng, “Physics-informed neural network for simulating magnetic field of coaxial magnetic gear,” Engineering Applications of Artificial Intelligence, vol. 136, 2024.
[5] M. Raissi, P. Perdikaris, and G. Karniadakis, “Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear PDEs,” Journal of Computational Physics, vol. 378, pp. 686–707, 2019.
[6] Z. Li, N. Kovachki, K. Azizzadenesheli, et al., “Fourier neural operator for parametric partial differential equations,” SIAM Journal on Scientific Computing, vol. 43, no. 3, 2021.
[7] L. Lu, P. Jin, and G. Karniadakis, “DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem,” Nature Machine Intelligence, vol. 3, pp. 218–229, 2021.
[8] Brendel, V. Medvedev and A. Rosskopf, "Physics-Informed Neural Networks for Magnetostatic Problems on Axisymmetric Transformer Geometries," IEEE Journal of Emerging and Selected Topics in Industrial Electronics, vol. 5, no. 2, pp. 700-709, April 2024.
[9] Oh, S.; Hong, S.K. "Physics-Informed Neural Modeling of 2D Transient Electromagnetic Fields". Appl. Sci. 2025, 15, 12612.
[10] S. Hou, W. Wu and X. Hao, “Physics-informed neural network for simulating magnetic field of permanent magnet,” J. Phys.: Conf. Ser., vol. 2853, no. 1, 2024.
[11] Sun, Y., Xv, W. "Application of Physical Information Neural Network Based on Fourier Features in Electromagnetic Computing," Proceedings of the 1st Electrical Artificial Intelligence Conference, Volume 1. EAIC 2024. Lecture Notes in Electrical Engineering, vol 1394. Springer, Singapore.
[12] Z. Zhao, X. Guo, Y. Zhang and S. Xiao, "A Comprehensive Overview on Artificial Intelligence Applied in Electromagnetic Design," 2025 5th International Conference on Neural Networks, Information and Communication Engineering (NNICE), Guangzhou, China, 2025, pp. 1236-1240.
[13] O. Noakoasteen, S. Wang, Z. Peng, and C. Christodoulou, "Physics-Informed Deep Neural Networks for Transient Electromagnetic Analysis," IEEE Open Journal of Antennas and Propagation, vol. 1, pp. 404-412, 2020.
[14] Seho Son, Hyunseung Lee, Dayeon Jeong, Ki-Yong Oh, Kyung Ho Sun, "A novel physics-informed neural network for modeling electromagnetism of a permanent magnet synchronous motor," Advanced Engineering Informatics, Volume 57, 2023.
Citation: S. Magdaleno, "AI for Electromagnetic Simulations: Speeding up the Future of the Electromagnetic Simulations," Salvador Consultant.