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

TL;DR

The paper tackles the inverse problem of reconstructing a one-dimensional rough surface profile $h(x)$ from electromagnetic field measurements. It introduces a physics-informed neural network (PINN) that represents $h(x)$ and uses automatic differentiation to obtain $\partial h/\partial x$ and $\partial^2 h/\partial x^2$, while the scattered field is computed by the method of moments (MOM) and matched to data. The method is unsupervised and supports both full scattered-field data and phaseless total-field data for TE (Dirichlet) and TM (Neumann) cases, validated on Gaussian-correlated surfaces across noise, scale, height, wavenumber, and incidence regimes. Results show accurate surface recovery and robustness, indicating potential for fast, physics-consistent inverse sensing and extension to 3D problems.

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.

Figures (10)

• Figure 1: An illustrative figure for the PINN-based neural network to reconstruct rough surfaces from field data.
• Figure 2: Reconstruction of rough surfaces against the actual surfaces for case A (known full scattered data) without noise.
• Figure 3: Reconstruction of rough surfaces against the actual surfaces for case B (known phaseless total field data) without noise.
• Figure 4: Reconstruction of rough surfaces compared to actual surfaces using data with different noise levels $\epsilon$ in the case A of known scattered field data for TE and TM fields.
• Figure 5: Reconstruction of rough surfaces compared to actual surfaces with respect to different noise levels $\epsilon$ in the case B of known phaseless total field data for TE and TM fields.