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Inverse problems often occur in nuclear physics, when an unknown potential has to be determined from observables such as cross sections or phase shifts. In this talk I propose two data-driven methods, using Volterra series and Neural Networks, where the scattering potentials can be estimated with good accuracy from experimentally available data in the Fourier domain and in position space as well. The Neural Network model is then used to describe the low energy 3S1 NN scattering at fixed angular momenta, giving a result within a few percent relative errors for the re-calculated phase shifts in a wide range of laboratory energies. The extension of the model for the fixed energy and varied angular momenta case will also be addressed.