  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 via 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, rather only the field data is used. Both TE field
(Dirichlet boundary condition) and 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.
