We show a new approach for solving the N-body problems based on neural networks. Without loss of generality, we derived a network solution for the time-dependent positions of N bodies in self-gravitating systems. The simulation is limited to a system of collisionless disks-a case for determining the spatial distributions of dark matter and in reproducing global effects such as formation of spiral galaxies. Our approach yields a solution that is analytic with time-reversed path-tracing capabilities that could lead to new findings in the study of the collective behavior of N-body systems.