Clustering and Uncertainty Analysis to Improve the Machine
  Learning-based Predictions of SAFARI-1 Control Follower Assembly Axial
  Neutron Flux Profiles
Lesego Moloko Pavel Bokov Xu Wu Kostadin Ivanov
The goal of this work is to develop accurate Machine Learning (ML) models for
predicting the assembly axial neutron flux profiles in the SAFARI-1 research
reactor, trained by measurement data from historical cycles. The data-driven
nature of ML models makes them susceptible to uncertainties which are
introduced by sources such as noise in training data, incomplete coverage of
the domain, extrapolation and imperfect model architectures. To this end, we
also aim at quantifying the approximation uncertainties of the ML model
predictions. Previous work using Deep Neural Networks (DNNs) has been
successful for fuel assemblies in SAFARI-1, however, not as accurate for
control follower assemblies. The aim of this work is to improve the ML models
for the control assemblies by a combination of supervised and unsupervised ML
algorithms. The $k$-means and Affinity Propagation unsupervised ML algorithms
are employed to identify clusters in the set of the measured axial neutron flux
profiles. Then, regression-based supervised ML models using DNN (with
prediction uncertainties quantified with Monte Carlo dropout) and Gaussian
Process (GP) are trained for different clusters and the prediction uncertainty
is estimated. It was found that applying the proposed procedure improves the
prediction accuracy for the control assemblies and reduces the prediction
uncertainty. Flux shapes predicted by DNN and GP are very close, and the
overall accuracy became comparable to the fuel assemblies. The prediction
uncertainty is however smaller for GP models.