High-fidelity models are computationally intensive to work with in many-query applications, such as the design process of small modular reactors. A reduced order model of the high-fidelity model can still accurately determine the quantities of interest with only a fraction of the computational cost, and thus can potentially solve the aforementioned problem. However, reducing a high-fidelity model of a small modular reactor is complicated due to the large number of parameters involved in nuclear reactor models, as that leads to an exponentially increasing parameter space needed to be surveyed.

Disregarding the parameters with the smallest impact on the output and thereby reducing the total number of variables can limit the parameter space, and thus speed up the model reduction at the cost of some accuracy. Perturbation theory utilizes the benefits of adjoint theory to efficiently determine sensitivities of responses to all the variables in the model, which allows one to find the influence on the output of the different variables without the need for evaluating them all repeatedly. It is then possible to apply a reduced order modeling technique such as proper orthogonal decomposition to determine and select only the most important eigenmodes of the high-fidelity model and build a reduced model.

This approach is applied to three different neutronics model of the U-Battery, varying in complexity. The presented method has shown to alleviate computational cost significantly for all examined reduced models. However, the upfront cost of building the reduced models by sampling the high-fidelity models has been considerable, especially when evaluating the resulting accuracy of the reduced models. A proper selection of the proper orthogonal decomposition tolerances must be made to ensure sufficient accuracy and to prevent oversampling. Nonetheless, combining proper orthogonal decomposition with perturbation theory showed to be a promising way of selecting only a few parameters for participation in the building of reduced order models while minimizing the loss of accuracy compared to the high-fidelity model.