  Solving electromagnetic inverse scattering problems (ISPs) is challenging due
to the intrinsic nonlinearity, ill-posedness, and expensive computational cost.
Recently, deep neural network (DNN) techniques have been successfully applied
on ISPs and shown potential of superior imaging over conventional methods. In
this paper, we analyse the analogy between DNN solvers and traditional
iterative algorithms and discuss how important physical phenomena cannot be
effectively incorporated in the training process. We show the importance of
including near-field priors in the learning process of DNNs. To this end, we
propose new designs of loss functions which incorporate multiple-scattering
based near-field quantities (such as scattered fields or induced currents
within domain of interest). Effects of physics-guided loss functions are
studied using a variety of numerical experiments. Pros and cons of the
investigated ISP solvers with different loss functions are summarized.
