Quantification of neural networks uncertainties with applications to SAFARI-1 axial neutron flux profiles
Deep Neural Networks (DNNs) have been widely used as a data-driven modelling tool in nuclear engineering. However, as a Machine Learning model, Artificial Neural Network (ANN) predictions are subjected to uncertainties originating from the noise in training data, incomplete coverage of the domain, and imperfect neural network architectures. In this work, we target at quantifying the prediction/approximation uncertainties of ANNs using Monte Carlo Dropout (MCD), as well as Bayesian Neural Networks (BNNs) which are solved by variational inference. With a demonstration problem in which neural networks are used to predict the assembly axial neutron flux profiles, the results have shown that the three different neural network models (regular DNNs, DNNs solved with MCD and BNNs) can produce results that agree very well among each other and with the measurement data, on cycles that are not used in the training process. Besides the excellent generalization capability, the uncertainty bands produced by MCD and BNN agree very well, and in general, they can fully envelop the noisy measurement data points. (authors)