Application and comparison of several adaptive sampling algorithms in reduced order modeling

Model Order Reduction (MOR) techniques have extensive applications across scientific and engineering disciplines, such as neutron field reconstruction of nuclear reactor cores, thermoelastic field reconstruction, fluid, and solid mechanics. In the process of building a Reduced Order Model (ROM), the selection of the basis functions in the offline stage is crucial and directly depends on the parameter space sampling strategy. This problem has always been a challenge in MOR. Research into adaptive sampling algorithms has become a hot topic in recent years. To better understand the application of these algorithms to MOR, this paper focuses on three prevalent adaptive sampling algorithms: pseudo-gradient sampling, adaptive sparse grid sampling, adaptive training set extension. These have been successfully applied in various applications, including nuclear reactor cores, molten salt reactor system, power system for convection problems. We systematically assess and compare their performance, finding that adaptive sampling algorithms excel in sampling divergent and oscillating areas and are generally better than the standard sampling strategy. Specifically, the pseudo-gradient sampling algorithm is effective for small-scale scenarios, while the other two algorithms are designed for large-scale sampling. Their practicality is confirmed through successful applications in nuclear reactor cores.