We present a physically-primed deep-neural-network (DNN) architecture for undersampled MRI reconstruction. Our architecture encodes the undersampling mask in addition to the observed data. It employs an appropriate training approach that uses undersampling mask augmentation to encourage the model to generalize the undersampled MRI reconstruction problem. We demonstrated an enhanced generalization capacity which resulted in significantly improved robustness against variations in the acquisition process and the anatomical distribution, especially in pathological regions.