Reduced order modelling (ROM) in engineering has rapidly become of
great interest, yielding potential of speed up while maintaining high fidelity.
Practical problems involving neutron diffusion, scattering and shielding have
particularly complex multi-scale behaviour in energy and space making real time, multi-query, design or data assimilation applications are beginning to benefit from ROM research. This is typically done via Proper Orthogonal Decomposition (POD), coupled with Galerkin projection. In this thesis we demonstrate multiple novel approaches to Non-intrusive reduced order modelling (NIROMs). We apply them to two research areas, shielding and neutron diffusion.

First a novel way of using reduced order models (ROMs) in a coupling scheme
to model more complex material configurations from a library of individual
material reduced order models (ROMs) is presented. Secondly this framework
is generalised to n-group and validated with a 2-group shielding benchmark.
Finally the lack of guaranteed conservative NIROM solutions is addressed and
demonstrated with variants of the Advection-Diffusion equation, achieved
through a novel Sub-Grid Scale ROM (SGS ROM) to add conservation and
resolution to ROM solutions.