  We apply dynamic mode decomposition (DMD) and proper orthogonal decomposition
(POD) methods to flows in highly-heterogeneous porous media to extract the
dominant coherent structures and derive reduced-order models via Galerkin
projection. Permeability fields with high contrast are considered to
investigate the capability of these techniques to capture the main flow
features and forecast the flow evolution within a certain accuracy. A DMD-based
approach shows a better predictive capability due to its ability to accurately
extract the information relevant to long-time dynamics, in particular, the
slowly-decaying eigenmodes corresponding to largest eigenvalues. Our study
enables a better understanding of the strengths and weaknesses of the
applicability of these techniques for flows in high-contrast porous media.
Furthermore, we discuss the robustness of DMD- and POD-based reduced-order
models with respect to variations in initial conditions, permeability fields,
and forcing terms.
