This paper proposes a fully-connected artificial neural network (ANN) approach for addressing the full-wave inverse scattering problem in a quantitative fashion. The proposed scheme processes the scattered field samples collected at receivers locations and provides as output an estimate of the unknown complex permittivity in strongly non-linear scenarios. The proposed approach requires a proper training step, which is also addressed via an automatic randomly-shaped complex profile generator inspired by the statistical distribution of breast biological tissues, and is almost real-time in the recovery step. Several representative numerical tests were carried out to evaluate the performance of the proposed method and to validate the use of ANN for quantitative imaging purposes in biological-inspired scenarios.