The inverse problem of estimating the refractive index in a waveguide based on wave field measurement data is studied. A differentiable finite-difference scheme for the parabolic wave equation is constructed. The desired function of spatial coordinates, corresponding to the refractive index, is represented as a deep neural network. Optimization problem with respect to unknown refractive index function is formulated and solved. Automatic differentiation of the numerical scheme is used for efficient gradient computation. Numerical examples confirm that the proposed method outperforms the existing approaches to solving underwater and tropospheric tomography problems.