The rapidly developing field of artificial intelligence (AI) has made significant advancements in areas such as image processing, language, decision-making, and diagnostics, providing new methods for solving complex problems. The increasing intelligence of electrical equipment, combined with the coupling of strong and weak electrical fields, has led to the emergence of multi-scale, multi-physical field coupling and nonlinear problems in electromagnetic fields. High-precision numerical modeling and optimization are increasingly challenging.

Therefore, this paper combines recent research outcomes from the author’s team to introduce deep learning methods for solving typical interdisciplinary problems, such as data-driven modeling, physics-driven PDE solving, and knowledge-embedding modeling. In particular, the paper discusses the current state of intelligent modeling for complex electromagnetic field problems driven by both data and knowledge. It also offers perspectives on the scientific challenges and important future directions in the research and engineering implementation of electromagnetic field intelligent modeling.

In the area of data-driven modeling, the paper explores its application in the performance analysis and optimization of electrical equipment. The discussion is divided into three parts: performance parameter calculation, electromagnetic thermal field prediction, and knowledge discovery modeling. By combining numerical simulation and experimental data, deep learning algorithms can mine potential knowledge from the data, enabling rapid computation of one-dimensional performance and two- and three-dimensional fields. This approach allows for real-time simulation of local performance, global performance, and micro characteristics.

Regarding physics-driven partial differential equation (PDE) solving, the paper discusses two main research directions: knowledge-embedding regularization methods and designing machine learning model structures based on physical meaning. Constructing loss functions or network structures that align with physical laws makesit possible to solve PDEs without relying on sample data. This method is beneficial when physical conditions are incomplete and sample data is scarce. Using AI to solve physical equations helps overcome traditional bottlenecks, improving computational efficiency and expanding application scope.

In the area of knowledge-embedding modeling, the paper discusses how to implicitly integrate domain knowledge, mainly through multi-fidelity models and neural network operator methods, to improve the precision and efficiency of computational models. By embedding the knowledge inherent in high-precision samples into the model, high-precision forward and inverse problem models can be built. As data accumulates, the model's accuracy and generalization ability will improve. This method fully utilizes the advantages of deep learning and integrates basic physical theories. As data grows, knowledge-embedding methods are expected to be crucial in solving more complex electromagnetic field problems and enhancing overall simulation outcomes.

In conclusion, the fusion of AI and knowledge has become a significant trend in the development of numerical simulation. Integrating data-driven, physics-driven, and knowledge-embedding methods has accelerated the advancement of electromagnetic field modeling and optimization. These methods have improved simulation accuracy and expanded the application range of numerical simulations for complex electromagnetic field problems. However, the exploration of AI in numerical simulation is still in its early stages, facing challenges such as insufficient model generalization, computational efficiency improvement, and physical constraint integration. Future research should focus on addressing these issues to promote the broader application and development of AI in the field of electromagnetic field numerical simulation.