A Preliminary Study on the Use of the Linear Regression Method for Multigroup Cross-Section Interpretation

Computational modeling and simulations are widely used for evaluation of the performance and safety features of innovative nuclear reactor designs. Multigroup-based deterministic neutronics codes are often employed in these reactor design calculations because they can provide fast predictions of the neutron flux distribution and other neutronics characteristic parameters. Nevertheless, providing accurate multigroup cross sections for deterministic codes is an onerous job, which makes establishing an exhaustive cross-section library computationally prohibitive. Partly because of these reasons, multigroup neutron cross sections are normally stored only at certainty state points in the data library of these deterministic codes, and linear interpolation methodology is commonly utilized to estimate the cross sections at unknown states. However, the applicability of linear interpolation is limited, and the precision of its results is moderate.

In this paper, we discuss a preliminary feasibility study that we performed on providing more precise multigroup cross sections for deterministic neutronics codes by using the linear regression methodology. Compared to the traditional linear interpolation method, the linear regression approach principally showed improved computational efficiency considering the use of more data in the cross-section library, and constructed hypothesis functions for the responses of interest with a higher order of accuracy. In this study, a case study on Lightbridge Corporation’s metallic fuel element was carried out to demonstrate the feasibility and advantages of linear regression in multigroup cross-section interpretation. A reference cross-section library was established through calculations conducted with the Monte Carlo neutronic code Serpent. Because of the preliminary nature of this feasibility study, only the macroscopic total cross section is considered. Linear interpolation and linear regression were both used to estimate cross sections at unknown states based on the data available in the library. By comparing the performance of both methodologies, we demonstrated that the linear regression methodology achieved wider applicability and better precision in cross-section interpretation. Moreover, the linear regression process was finished within 15 s using a single processor core, which indicated that the additional computational burden brought by the implementation of linear regression methodology in the task was acceptable.