Accurate prediction of the thermospheric density field has recently been gaining a lot of attention, due to an outstanding increase in space operations in Low-Earth Orbit, in the context of the NewSpace. In order to model such high-dimensional systems, Reduced-Order Models (ROMs) have been developed against existing physics-based density models. In general, the data-driven reconstruction of dynamical systems usually consists of two steps: compression and prediction. In this paper, we focus on the compression step and assess state-of-the-art order reduction methodologies such as autoencoders, linear, and nonlinear Principal Component Analysis (PCA). Kernel-based PCA, which is a nonlinear variation of PCA, outperforms Neural Networks in representing the model in low-dimensional space in terms of accuracy, computational time, and energy consumption for both the Lorenz system, a chaotic dynamical system developed in the context of atmospheric modeling, and the thermospheric density.