Before revision:  An energy preserving, computationally efficient reduced-order model (ROM) is constructed by proper orthogonal decomposition (POD) with the Galerkin projection  .
After revision:  An energy preserving, computationally efficient reduced-order model (ROM) is constructed in the same way as the full order model (FOM), preserving the reduced skew-symmetric structure and integrating in time with the AVF method. Relying on structure-preserving discretizations in space and time and applying proper orthogonal decomposition (POD) with the Galerkin projection .