Subspace methods for multi-physics reduced order modeling in nuclear engineering applications

This manuscript proposes a new extension to a reduced order modeling algorithm, previously introduced for single-physics models, to multi-physics models. This manuscript focuses on loosely-coupled physics models wherein the output of one physics model is fed as input to the next physics model, and each physics model is solved separately while freezing all other physics models. The idea is to perform three reductions at each physics-to-physics interface, one based on the upstream physics, another for the downstream physics, and a third for the interaction thereof. Accurately capturing the interaction between the reduced physics models is an essential feature of the proposed algorithm, and will be the key measure for its success. For standard model execution, this interaction is often captured using an iterative technique that loops over the different physics until convergence or meeting some stopping criterion. We adopt a similar approach in which the effective dimensionality of each physics-to-physics interface is updated iteratively until a user-defined error tolerance is met. A quarter PWR fuel assembly depleted to 32 GWD/MTU by iteratively solving the quasi-static transport-depletion approximation is used to exemplify the application of the proposed algorithm. Active subspaces for the nuclear cross-sections and neutron flux are determined, and compared to the active subspaces obtained without the physics coupling.