Preliminary Evaluation of the LASSO Method for Prediction of the Relative Power Density Distribution in Mixed Oxide (Pu, DU)O₂ Fuel Pellets

Predicting the power distribution within nuclear fuel is essential for predicting reactor fuel performance, since power distributions can impact pellet temperature distributions and fission product transport and migration. Analytical expressions for radial power distribution in fuel pellets were sought using lattice physics calculations to generate data and a machine learning technique to find representative expressions. Analytical approximations can be useful in nuclear fuel performance codes, such as element simulation and stresses (ELESTRES)/ element simulation code in a loss of coolant accident (ELOCA) for providing very rapid predictions of power distributions with reduced computational effort and memory requirements, relative to using an embedded or coupled neutron transport/burnup reactor physics code. Radial power distributions were calculated a priori using lattice physics codes to model mixed oxide (MOX) 37-element fuel bundles in pressure tube heavy water reactors. Such advanced fuels are of interest for future fuel cycles. Several datasets were generated with different amounts of PuO₂ and variable neutron energy spectrum. Results of preliminary studies with the least absolute shrinkage and selection operator (LASSO) regression machine learning method have obtained analytical fitting functions with a mean maximum relative error (MRE) of 0.056 and a maximum MRE of 0.152 on the test set. However, using LASSO to estimate the coefficients of a physically motivated modified Bessel plus an exponential function, results in a lower MRE (mean MRE 0.041 and maximum MRE 0.11) on the same test set. Further potential improvements in both the curve fit and the machine learning methods are discussed.