This work addresses the computational difficulties involved with the simulation of the nonlinear ring oscillator system. Simplified Reduced Order Model is constructed which leads to faster simulation. Snapshot-based ROM is usually used due to its numerous advantages. In this study, two different sets of snapshot matrices of the ring oscillator model are constructed. The discrete empirical interpolation method is proposed to nonlinear ring oscillator model under different scenarios. The ROM is validated and found to be accurate with an acceptable error bound, and result in faster simulation.