Surface profile recovery from electromagnetic field with physics--informed neural networks

TL;DR

This paper presents a physics-informed neural network approach to reconstruct one-dimensional rough surfaces from electromagnetic field data, demonstrating high accuracy and robustness without requiring surface data for training.

Contribution

The paper introduces an unsupervised PINN-based method for surface reconstruction from electromagnetic data, applicable to both TE and TM fields, and capable of using phaseless data.

Findings

Accurately reconstructs rough surfaces from electromagnetic field data.

Robust performance across various problem regimes.

Effective with both full and phaseless field data.

Abstract

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.