Deep learning

Physics

Finite element method

Mathematics

Engineering physics

Evolutionary biology

Biology

Partial differential equation

Function (biology)

Boundary value problem

Artificial intelligence

Physical law

Programming language

Computational electromagnetics

Electromagnetic field

Solver

Electromagnetics

Computer science

Quantum mechanics

Applied mathematics

Artificial neural network

Boundary element method

Thermodynamics

IEEE Transactions on Magnetics

Deep learning has achieved remarkable success in diverse applications; however, its use in solving partial differential equations (PDEs) has emerged only recently. Here, we present a feasibility study of applying physics-informed deep learning methods for solving PDEs related to the physical laws of electromagnetics. The methodology uses automatic differentiation, and the loss function is formulated based on the underlying PDE and boundary conditions. The feasibility of the method is shown using three electromagnetic problems of varying complexity and the results show close agreement with the ground truth from a finite-element analysis solver. The application of transfer learning is also explored and results in faster training. Furthermore, a hybrid approach involving physics-based governing equations and labeled data is also introduced to improve the accuracy of the results.

Physics Informed Neural Networks for Electromagnetic Analysis