GRINN (Gravity Informed Neural Network) solves the coupled set of time-dependent partial differential equations describing the evolution of self-gravitating flows in one, two, and three spatial dimensions. It is based on physics informed neural networks (PINNs), which are mesh-free and offer a fundamentally different approach to solving such partial differential equations. GRINN has solved for the evolution of self-gravitating, small-amplitude perturbations and long-wavelength perturbations and, when modeling 3D astrophysical flows, provides accuracy on par with finite difference (FD) codes with an improvement in computational speed.