Application of Support Vector Regression in Estimation of Buildup Factors for Double-Layered Shields

The point kernel method is a widely used method for gamma ray dose rate calculations in shielding design. Buildup factors are key parameters for the point kernel method. Therefore, a great effort has been made in the past to find compact mathematical expressions producing accurate buildup factor estimates for embedding into point kernel codes. The expressions for single material buildup factor are generally well defined and understood, while for the stratified, multi-layer shields, which are mostly used in nuclear facilities, existing solutions are few, and are certainly not that compact, and are of limited applicability, usually only for certain material combinations. The problem of determination of buildup factors for multi-layer shields has been approached by introducing semi-empirical formulas, having a number of parameters, which are fitted to the results of detailed Monte Carlo calculations. This “ traditional” approach requires an ad-hoc definition of the structure of the fitting function. Instead of developing a new formula for multi-layer shields we investigate the applicability of a machine learning approach to this problem. We employed a rather recently introduced machine learning technique, Support Vector Regression (SVR), which has a strong theoretical background in statistical learning theory, developed by Vapnik (1). Superior empirical performance of the method has been reported on difficult regression problems in different fields of science and technology. SVR is a data driven, kernel based nonlinear modeling paradigm in which model parameters are automatically determined by solving a quadratic optimization problem. The main objective of the work reported in this paper was to evaluate the possibility of applying the Support Vector Regression method for modeling and calculating buildup factors for double layer shields. The starting set of experimental data, for training and testing of the machine learning algorithm, was obtained by Monte Carlo calculations performed by SAS3 sequence of the SCALE code package. We illustrate the performance of the solution and discuss its applicability in routine point-kernel codes as fast and accurate method for calculating buildup factors of double-layer shields composed of different combinations of materials.