This paper introduces a structured neural network (StNN) for realizing states of dynamical systems by leveraging data-driven learning.The StNN utilizes a low-complexity operator called the Hankel operator, derived from time-delay measurements, to solve dynamical systems.Numerical simulations comparing the StNN with other techniques show that it reduces the number of parameters and computational complexity.The proposed StNN enables the prediction and understanding of future states in state-space dynamical systems.