  This work discusses the model reduction problem for large-scale
multi-symplectic PDEs with cubic invariants. For this, we present a linearly
implicit global energy-preserving method to construct reduced-order models.
This allows to construct reduced-order models in the form of Hamiltonian
systems suitable for long-time integration. Furthermore, We prove that the
constructed reduced-order models preserve global energy, and the spatially
discrete equations also preserve the spatially-discrete local energy
conversation law. We illustrate the efficiency of the proposed method using
three numerical examples, namely a linear wave equation, the Korteweg-de Vries
equation, and the Camassa-Holm equation, and present a comparison with the
classical POD-Galerkin method.
