A hybrid Monte Carlo–nodal–machine learning framework for fast intra-pin power prediction in the PRATIC benchmark

Accurate prediction of intra-pin power distributions can be challenging for state-of-art nodal diffusion solvers, particularly in cores exhibiting strong spatial heterogeneities such as boron-free small modular reactors. Under such conditions, pin power reconstruction methods may not fully capture the potential presence of highly localised flux gradients, leading to biased heat flux and neutron fluence estimates. While Monte Carlo methods can resolve these effects, their computational cost limits their applicability for routine core-follow analyses. This work investigates data-driven surrogate models as a computationally efficient alternative to MC simulations for intra-pin power estimation. The study is based on a depletion calculation of a two-dimensional version of the PRATIC boron-free PWR SMR benchmark, analysed within the Kraken multi-physics framework. For that purpose, the core was consistently modelled with the MC Serpent code and the ANTS diffusion solver to generate a detailed intra-pin power dataset used for surrogate model training under nominal operating conditions. Two modelling approaches were considered: a multivariate linear regression model and a feed-forward neural network (NN), both using rapidly available nodal outputs such as pin power or pin burnup as input. The linear model achieved a coefficient of determination of R 2 = 0.97030 on the test dataset, indicating reasonable predictive capability but limited ability to capture nonlinearity effects. In contrast, the NN significantly improved performance, achieving a R 2 = 0.99962 and reducing the root mean square error by nearly an order of magnitude. The NN predictions showed excellent agreement with MC reference data, with a mean relative deviation of ( 0.02 ± 0.85 ) % , while maintaining prediction times on the order of seconds compared to several days for MC simulations. This study demonstrates the potential of surrogate models to provide rapid intra-pin power estimates across burnup states for the investigated benchmark within the validity envelope of the operating conditions used to generate the training dataset (all rod out, equilibrium xenon, fixed thermal-hydraulic conditions, and burnup states up to 17.5 MWd/kgU). Future developments incorporating a wider range of operating conditions and core states into the training dataset could further extend this validity envelope and enhance the model’s applicability to online core monitoring, as well as to the design, monitoring, and evaluation of fuel material irradiation programmes.