Applicability Analysis of Reduced-Order Methods with Proper Orthogonal Decomposition for Neutron Diffusion in Molten Salt Reactor

The high-dimensional integral–differential nature of the neutron transport equation and the complexity of nuclear reactors result in high computational costs. A set of reduced-order modeling frameworks based on Proper Orthogonal Decomposition (POD) is developed to improve the computational efficiency for neutron diffusion calculations while maintaining accuracy, especially for small samples. For modal coefficient calculations, three methods—Galerkin, radial basis function (RBF), and Deep Neural Network (DNN)—are introduced and analyzed for molten salt reactors. The results show that all three reduced-order models achieve sufficient accuracy, with neutron flux L2 errors below 1% and delayed neutron precursor (DNP) L2 errors below 2.4%, while the acceleration ratios exceed 800. Among these, the POD–Galerkin model demonstrates superior performance, achieving average L2 errors of less than 0.00658% for neutron flux and 1.01% for DNP concentration, with an acceleration ratio of approximately 1800 and excellent extrapolation ability. The POD–Galerkin reduced-order model significantly enhances the computational efficiency for solving neutron multi-group diffusion equations and DNP conservation equations in molten salt reactors while preserving the solution accuracy, making it ideal for a liquid fuel molten salt reactor in the case of small samples.