In this work, we reconstruct the cold and dense matter equation of state~(EoS) from the current observational neutron star data. We achieve this by using a physics-based deep learning method that utilizes the Automatic Differentiation technique. A deep neural network, {\it EoS Network}, is deployed to represent the EoS in a model-independent way. A second neural network, the {\it TOV-Solver Network}, is trained to solve the Tolman–Oppenheimer–Volkoff~(TOV) equations. The {\it EoS Network} is then combined with the pre-trained {\it TOV-Solver Network} and a gradient-based approach is implemented to optimize the weights of the {\it EoS Network}, in an unsupervised manner. Thus, the designed pipeline is trained to optimize the EoS, so as to yield through TOV equations, a mass-radius~(M-R) curve that best fits the observations. We present the EoS obtained from this procedure, using the current neutron star observational data. The results are compatible with the reconstructions from earlier works that used conventional methods and also with the limits of tidal deformability obtained from the gravitational wave event, GW170817.