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.

Development and application of a new random walk model to simulate the transport of degradable pollutants

To simulate the pollutant transport with seif-purification in inland waters,the widely used random walk model(RWM)is modified to include a source term for the degradation and to consider the impact of land boundaries.The source term for the degradation is derived from the assumption of the first-order reaction kinetics.Parameters for the new model are determined by a comparison to the analytical results.The proposed model is then applied to simulate and analyze the transport of a test pollutant and its spatial distribution in a large reservoir in northeast China.Reasonable results are obtained,and the effects of the runoff,the flow structure,and the wind on the pollutant transport are analyzed.The results may help the risk assessment and the management of the water pollution in inland waters.