Deep Image Prior Enabled Two-Dimensional Electromagnetic Computation

Supervised deep learning has shown promising progress in accurate and efficient electromagnetic modeling. However, a significant challenge arises when employing neural networks (NNs) in electromagnetic computations, as they typically require a substantial amount of training data, which are often not readily available.To address the problems associated with data training, we propose an unsupervised deep image prior (DIP) network for two-dimensional (2D) electromagnetic computations, which consists of three main components: an encoder, a decoder, and skip connections. The input data is only one low-resolution portrait of the fields generated through the 2D finite-difference time-domain method (FDFD) and is directly utilized by the DIP network to predict the numerical solution of electromagnetic fields. The resulting output data represents the distribution of the electric field with high-resolution. Through numerical tests, the proposed DIP method presents great applicability and robustness for 2D scattering problems involving scatterers with varying shapes and material properties, including relative permittivity, relative permeability, and electric conductivity. Utilizing a field distribution defined on a coarse mesh, the DIP network is capable of outputting a field distribution with accuracy comparable to that of a dense mesh. For instance, when provided with input data at a sampling density of 10 points per wavelength (PPW), the DIP method significantly enhances the original FDFD result at the same sampling density, achieving near-equivalence with the accuracy of FDFD with 20 PPW. Compared to previous research on the application of NNs in electromagnetic computation, which often relies on high-quality and generalizable data for training, our approach utilizing the FDFD method in conjunction with the DIP network allows for fast and precise computation of the 2D electromagnetic field distribution without the need for training data. The DIP method introduces novel directions and possibilities for research and applications within the domain of numerical computation of electromagnetic fields.