In this paper, the capabilities of reduced order methods, with application to nuclear reactor core spatial dynamics, are presented. The potential of reduced order methods with respect to the classical Modal Method approach is firstly addressed. In particular, two modelling approaches based on a Modal Method and on the Proper Orthogonal Decomposition technique, for developing a control-oriented model of nuclear reactor spatial kinetics, are compared. Subsequently, the Reduced Basis method for simulating, in a rapid and reliable way, the movement of control rods is addressed, solving parametrized multi-group neutron diffusion equations both in the time-dependent and stationary formulations. For the latter case, a different sampling technique, within the Reduced Basis framework, has been employed, namely, the centroidal Voronoi tessellation, which allows for a hierarchical parameters space exploration, without relying on an a posteriori error estimation. In this way, the Offline computational time might be sensibly reduced. Finally, a preliminary multi-physics reduced order model of a Lead Fast Reactor single-channel is proposed as proof of concept in order to highlight the potential of reduced order methods in a many-query context.
