Gaussian processes for surrogate modeling of discharged fuel nuclide compositions

Abstract

Several applications such as nuclear forensics, nuclear fuel cycle simulations and sensitivity analysis require methods to quickly compute spent fuel nuclide compositions for various irradiation histories. Traditionally, this has been done by interpolating between one-group cross-sections that have been pre-computed from nuclear reactor simulations for a grid of input parameters, using fits such as Cubic Spline. We propose the use of Gaussian Processes (GP) to create surrogate models, which not only provide nuclide compositions, but also the gradient and estimates of their prediction uncertainty. The former is useful for applications such as forward and inverse optimization problems, the latter for uncertainty quantification applications. For this purpose, we compare GP-based surrogate model performance with Cubic-Spline-based interpolators based on infinite lattice simulations of a CANDU 6 nuclear reactor using the SERPENT 2 code, considering burnup and temperature as single dimensional input parameters resulting in a 2D study. Additionally, we compare the performance of uniform grid sampling to quasirandom sampling based on the Sobol sequence. We find that GP-based models perform significantly better in predicting spent fuel compositions than Cubic-Spline-based models on both sampling schemes. Uniform grid sampling performs better than quasirandom sampling in our 2D study, this cannot be generalized to higher dimensions. We have found that GP models require more time to compute a prediction. Although. A. AA a relatively small time (O ms), iterative methods used for statistical inference benefit from as-low-as-possible calculation times. Furthermore, we show that the predicted nuclide uncertainties are reasonably accurate. While in the studied two-dimensional case, grid- and quasirandom sampling provide similar results, quasirandom sampling will be a more effective strategy in higher-dimensional cases.