Predicting neutron diffusion eigenvalues with a query-based adaptive neural architecture

A query-based approach for adaptively retraining and restructuring a two-hidden-layer artificial neural network (ANN) has been developed for the speedy prediction of the fundamental mode eigenvalue of the neutron diffusion equation, a standard nuclear reactor core design calculation which normally requires the iterative solution of a large-scale system of nonlinear partial differential equations (PDE's). The approach developed focuses primarily upon the adaptive selection of training and cross-validation data and on artificial neural-network (ANN) architecture adjustments, with the objective of improving the accuracy and generalization properties of ANN-based neutron diffusion eigenvalue predictions. For illustration, the performance of a 'bare bones' feedforward multilayer perceptron (MLP) is upgraded through a variety of techniques; namely, nonrandom initial training set selection, adjoint function input weighting, teacher-student membership and equivalence queries for generation of appropriate training data, and a dynamic node architecture (DNA) implementation. The global methodology is flexible in that it can 'wrap around' any specific training algorithm selected for the static calculations (i.e., training iterations with a fixed training set and architecture). Finally, the improvements obtained are carefully contrasted against past works reported in the literature. Index Terms - ANN, DNA, eigenvalues, membership and equivalence queries, MLP, neutron diffusion.