Predicting Model Biases of the APOLLO3 Neutronics Code Using Machine Learning: Toward a Multiscale and Multifidelity Approach

Abstract

As part of the verification, validation, and uncertainty quantification process applied to neutronics deterministic codes, there is a requirement to expand the validation domain, especially to accommodate new third-generation reactors. The objective of the present work is to estimate the numerical biases arising from the several approximations used in deterministic codes and across different points in the phase space. Typically, this is accomplished by comparing the deterministic code to be validated with a Monte Carlo or stochastic reference code (without significant approximations). Since these reference calculations are computationally expensive, this paper proposes an alternative approach for predicting model biases of the APOLLO3® deterministic code for third-generation pressurized water reactors using machine learning algorithms. Three types of metamodels are employed (polynomial regression, kriging, and neural networks). Two scales are investigated, from a single assembly to a cluster of 3 × 3 assemblies [small two-dimensional (2-D) core], with model biases evaluated for APOLLO3 schemes with various levels of accuracy (lattice and core solvers, with high- to low-fidelity approaches). For the small 2-D core, numerical biases are observed for reactivity and power peak, representing both global and local quantities of interest. Throughout the study, the best results are achieved using kriging or neural networks, even if polynomial regression provides satisfactory predictions in some cases. The possibility of predicting biases for different quantities is also introduced. In conclusion, this paper discusses the prospects of extending the applicability of these metamodels to small and large third-generation pressurized water reactor cores, the idea being to potentially use these metamodels to support safety demonstrations for the new reactors in the long term.