Uncertainty Propagation in dynamical systems has gained importance in recent years, especially in the fields of astrodynamics and space applications. Areas such as space debris tracking, collision avoidance, and Cislunar operations can all benefit from uncertainty propagation. In this paper, a new method to propagate the dynamic system uncertainty using a state-space formulation-based neural network is introduced. To this end, the Radial Basis Function (RBF) approximation and the Mamba network are employed to predict the approximation coefficients pertaining to the future non-Gaussian PDF. The underlying assumption is the existence of a set of differential equations describing the time evolution of the RBF coefficients which approximate the PDF at predefined instances of time. Using this assumption, the Mamba network is trained using the first few sets of RBF approximation coefficients to predict the next sets of coefficients in the sequence. These coefficients are then used to generate the sequence of PDFs via interpolation. This approach bears some similarity to solving the Fokker-Planck equation which describes the evolution of the PDF of a dynamical system. The PDFs thus generated are compared with the PDFs from other methods such as Monte-Carlo simulation using information theoretic quantities such as Kullback-Liebler divergence.