Global energy preserving model reduction for multi-symplectic PDEs

Many Hamiltonian systems can be recast in multi-symplectic form. We develop a reduced-order model (ROM) for partial differential equations (PDEs) that preserves the global energy. The full-order solutions are obtained by finite difference discretization space and energy preserving average vector field (AVF) method. ROM is constructed same way as (FOM) applying proper orthogonal decomposition (POD) with Galerkin projection. system has structure FOM, discrete reduced Applying empirical interpolation method (DEIM), computed efficiently online stage. A priori error bound derived DEIM approximation to nonlinear Hamiltonian. accuracy computational efficiency of ROMs demonstrated Korteweg de Vries (KdV) equation, Zakharov-Kuznetzov (ZK) Schr{\"o}dinger (NLS) equation Preservation energies shows ensure long-term stability solutions.