Surface Profile Recovery from Electromagnetic Fields with Physics-Informed Neural Networks

Physics-informed neural networks (PINN) have shown their potential in solving both direct and inverse problems of partial differential equations. In this paper, we introduce a PINN-based deep learning approach to reconstruct one-dimensional rough surfaces from field data illuminated by an electromagnetic incident wave. In the proposed algorithm, the rough surface is approximated by a neural network, with which the spatial derivatives of surface function can be obtained via automatic differentiation, and then the scattered field can be calculated using the method of moments. The neural network is trained by minimizing the loss between the calculated and the observed field data. Furthermore, the proposed method is an unsupervised approach, independent of any surface data, where only the field data are used. Both transverse electric (TE) field (Dirichlet boundary condition) and transverse magnetic (TM) field (Neumann boundary condition) are considered. Two types of field data are used here: full-scattered field data and phaseless total field data. The performance of the method is verified by testing with Gaussian-correlated random rough surfaces. Numerical results demonstrate that the PINN-based method can recover rough surfaces with great accuracy and is robust with respect to a wide range of problem regimes.