Reactor field reconstruction from sparse and movable sensors using Voronoi tessellation-assisted convolutional neural networks

The aging of operational reactors leads to increased mechanical vibrations in the reactor interior.The vibration of the incore sensors near their nominal locations is a new problem for neutronic field reconstruction.Current field-reconstruction methods fail to handle spatially moving sensors.In this study,we propose a Voronoi tessellation technique in combination with convolutional neural networks to handle this challenge.Observations from movable in-core sensors were projected onto the same global field structure using Voronoi tessellation,holding the magnitude and location information of the sensors.General convolutional neural networks were used to learn maps from observations to the global field.The proposed method reconstructed multi-physics fields(including fast flux,thermal flux,and power rate)using observations from a single field(such as thermal flux).Numerical tests based on the IAEA benchmark demonstrated the potential of the proposed method in practical engineering applications,particularly within an amplitude of 5 cm around the nominal locations,which led to average relative errors below 5% and 10% in the L_(2) and L_(∞)norms,respectively.

Physics-constrained neural network for solving discontinuous interface K-eigenvalue problem with application to reactor physics

Machine learning-based modeling of reactor physics problems has attracted increasing interest in recent years.Despite some progress in one-dimensional problems,there is still a paucity of benchmark studies that are easy to solve using traditional numerical methods albeit still challenging using neural networks for a wide range of practical problems.We present two networks,namely the Generalized Inverse Power Method Neural Network(GIPMNN)and Physics-Constrained GIPMNN(PC-GIPIMNN)to solve K-eigenvalue problems in neutron diffusion theory.GIPMNN follows the main idea of the inverse power method and determines the lowest eigenvalue using an iterative method.The PC-GIPMNN additionally enforces conservative interface conditions for the neutron flux.Meanwhile,Deep Ritz Method(DRM)directly solves the smallest eigenvalue by minimizing the eigenvalue in Rayleigh quotient form.A comprehensive study was conducted using GIPMNN,PC-GIPMNN,and DRM to solve problems of complex spatial geometry with variant material domains from the fleld of nuclear reactor physics.The methods were compared with the standard flnite element method.The applicability and accuracy of the methods are reported and indicate that PC-GIPMNN outperforms GIPMNN and DRM.