  Particle-based simulations of the Vlasov equation typically require a large
number of particles, which leads to a high-dimensional system of ordinary
differential equations. Solving such systems is computationally very expensive,
especially when simulations for many different values of input parameters are
desired. In this work we compare several model reduction techniques and
demonstrate their applicability to numerical simulations of the Vlasov
equation. The necessity of symplectic model reduction algorithms is illustrated
with a simple numerical experiment.
