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Kinetic equations are crucial for modeling non-equilibrium phenomena, buttheir computational complexity is a challenge. This paper presents adata-driven approach using reduced order models (ROM) to efficiently modelnon-equilibrium flows in kinetic equations by comparing two ROM approaches:Proper Orthogonal Decomposition (POD) and autoencoder neural networks (AE).While AE initially demonstrate higher accuracy, POD's precision improves asmore modes are considered. Notably, our work recognizes that the classicalPOD-MOR approach, although capable of accurately representing the non-linearsolution manifold of the kinetic equation, may not provide a parsimonious modelof the data due to the inherently non-linear nature of the data manifold. Wedemonstrate how AEs are used in finding the intrinsic dimension of a system andto allow correlating the intrinsic quantities with macroscopic quantities thathave a physical interpretation.

Model Order Reduction for the 1D Boltzmann-BGK Equation: Identifying Intrinsic Variables Using Neural Networks