  In this paper, we propose the neural Born iterative method (NeuralBIM) for
solving 2D inverse scattering problems (ISPs) by drawing on the scheme of
physics-informed supervised residual learning (PhiSRL) to emulate the computing
process of the traditional Born iterative method (TBIM). NeuralBIM employs
independent convolutional neural networks (CNNs) to learn the alternate update
rules of two different candidate solutions regarding the residuals. Two
different schemes are presented in this paper, including the supervised and
unsupervised learning schemes. With the data set generated by the method of
moments (MoM), supervised NeuralBIM are trained with the knowledge of total
fields and contrasts. Unsupervised NeuralBIM is guided by the physics-embedded
objective function founding on the governing equations of ISPs, which results
in no requirement of total fields and contrasts for training. Numerical and
experimental results further validate the efficacy of NeuralBIM.
