  Deriving governing equations in Electromagnetic (EM) environment based on
first principles can be quite tough when there are some unknown sources of
noise and other uncertainties in the system. For nonlinear multiple-physics
electromagnetic systems, deep learning to solve these problems can achieve high
efficiency and accuracy. In this paper, we propose a deep learning neutral
network in combination with sparse regression to solve the hidden governing
equations in multiple-physics EM problem. Pareto analysis is also adopted to
preserve inversion as precise and simple as possible. This proposed network
architecture can discover a set of governing partial differential equations
(PDEs) based on few temporalspatial samples. The data-driven discovery method
for partial differential equations (PDEs) in electromagnetic field may also
contribute to solve more sophisticated problem which may not be solved by first
principles.
