Structure-preserving model reduction for dynamical systems with a first integral

Since the expense of the numerical integration of large scale dynamical systems is often computationally prohibitive, model reduction methods, which approximate such systems by simpler and much lower order ones, are often employed to reduce the computational effort. In this paper, we focus on dynamical systems with a first integral, which can always be written as skew-gradient systems. By focusing on and making use of the skew-gradient structure, we present structure-preserving model reduction approaches that yield efficient reduced-order systems while preserving the first integral.