The intricate nature of detailed kinetic mechanisms for plasmaassisted combustion motivates the development of high-fidelity surrogates to simplify their use in extensive numerical simulations. This paper presents a machine-learning approach based on the coupling of Principal Component Analysis (PCA) with Gaussian Process Regression (GPR) to produce a reliable reduced-order representation of the detailed plasmacombustion physics. The entire state-space is expressed in function of a selected number of principal components using a non-linear Gaussian regression model. This machine-learning framework allows for a superior dimensionality compression compared to conventional data-driven reduction strategies based solely on principal component analysis. The performance of the present technique is assessed for the simulation of ethylene-air ignition by nanosecond repetitive pulsed discharges at conditions relevant to supersonic combustion and flame holding in scramjet cavities: temperatures from 600 K to 1000 K, and a pressure of 0.5 atm.