Reduced-order methods for neutron transport kinetics problem based on proper orthogonal decomposition and dynamic mode decomposition

This work proposes two reduced -order methods to address the high computing resource consumption of neutron transport kinetics problems. The first method is based on proper orthogonal decomposition (POD), which integrates the POD basis with the governing equation. The second method is based on dynamic mode decomposition (DMD), which constructs an approximate linear relationship to predict the time -dependent physical quantities. Numerical results demonstrate that both two reduced -order methods can achieve high accuracy and efficient prediction. For the selected cases, POD can obtain a speed-up ratio of 105 - 429, while DMD can obtain a speed-up ratio of 2300 - 12500. For step transient situations, POD and DMD predict power errors do not exceed 0.42% and 0.05%. For ramp transient situations, POD and DMD predict power errors do not exceed 0.69% and 1.9%. This work can provide some useful suggestions for applications and further development in neutron transport kinetics reduced -order model.