Physics informed neural networks for electric field distribution characteristics analysis

Abstract

Abstract Electric field calculations based on the Poisson equation have been widely used in high voltage and plasma technology. However, in practical applications, the electric field distribution in space is relatively complex, and the simulation technology based on the traditional method is often a simplification of reality, which leads to a large error between the simulation and the actual measured value. In the actual application process, due to the limitation of measurement methods, it is necessary to infer the electric field data at other locations in space according to the measurement results. Physics informed neural networks (PINNs) are introduced into the electric field calculation. PINNs are considered partial differential equation solvers based on deep neural networks. In this paper, 2D and 3D electric field distributions are discussed and compared with the finite element method. A method of dividing the dielectric distribution based on the sigmoid function is proposed, which can be effectively used to construct the spatial electric field model of the homogeneous dielectric. The combination of the data and physical model based on PINNs establishes a method to solve the inverse problem of the relative permittivity in the electric field. The results show that PINNs can calculate the distribution of the electric field according to the physical equations and different types of constraints and parameters.