Modeling the non-linear relationship of the Magnetic Resonance (MR) signal and biophysical sources is computationally expensive and unstable using conventional methods. We develop an unsupervised physics-informed deep learning algorithm that quantifies MR parameters from multi-echo GRE data in a single computational pass. The algorithm produced accurate B0 and R2* field maps without phase wrapping artifacts and with typical contrast variations. The success of this network demonstrates the feasibility of physics-informed quantitative MRI (qMRI) without the need for ground truth training data, typically required by similar networks. This developed tool could provide fast and comprehensive tissue characterization in qMRI.