Kostadin Ivanov

Lesego E. Moloko, Pavel M. Bokov, Xu Wu et al.

Artificial Neural Networks (ANNs) have been successfully used in various nuclear engineering applications, such as predicting reactor physics parameters within reasonable time and with a high level of accuracy. Despite this success, they cannot provide information about the model prediction uncertainties, making it difficult to assess ANN prediction credibility, especially in extrapolated domains. In this study, Deep Neural Networks (DNNs) are used to predict the assembly axial neutron flux profiles in the SAFARI-1 research reactor, with quantified uncertainties in the ANN predictions and extrapolation to cycles not used in the training process. The training dataset consists of copper-wire activation measurements, the axial measurement locations and the measured control bank positions obtained from the reactor's historical cycles. Uncertainty Quantification of the regular DNN models' predictions is performed using Monte Carlo Dropout (MCD) and Bayesian Neural Networks solved by Variational Inference (BNN VI). The regular DNNs, DNNs solved with MCD and BNN VI results agree very well among each other as well as with the new measured dataset not used in the training process, thus indicating good prediction and generalization capability. The uncertainty bands produced by MCD and BNN VI agree very well, and in general, they can fully envelop the noisy measurement data points. The developed ANNs are useful in supporting the experimental measurements campaign and neutronics code Verification and Validation (V&V).

Xu Wu, Lesego E. Moloko, Pavel M. Bokov et al.

Machine learning (ML) has been leveraged to tackle a diverse range of tasks in almost all branches of nuclear engineering. Many of the successes in ML applications can be attributed to the recent performance breakthroughs in deep learning, the growing availability of computational power, data, and easy-to-use ML libraries. However, these empirical successes have often outpaced our formal understanding of the ML algorithms. An important but under-rated area is uncertainty quantification (UQ) of ML. ML-based models are subject to approximation uncertainty when they are used to make predictions, due to sources including but not limited to, data noise, data coverage, extrapolation, imperfect model architecture and the stochastic training process. The goal of this paper is to clearly explain and illustrate the importance of UQ of ML. We will elucidate the differences in the basic concepts of UQ of physics-based models and data-driven ML models. Various sources of uncertainties in physical modeling and data-driven modeling will be discussed, demonstrated, and compared. We will also present and demonstrate a few techniques to quantify the ML prediction uncertainties. Finally, we will discuss the need for building a verification, validation and UQ framework to establish ML credibility.

Lesego Moloko, Pavel Bokov, Xu Wu et al.

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.