  Recent performance breakthroughs in Artificial intelligence (AI) and Machine
learning (ML), especially advances in Deep learning (DL), the availability of
powerful, easy-to-use ML libraries (e.g., scikit-learn, TensorFlow, PyTorch.),
and increasing computational power have led to unprecedented interest in AI/ML
among nuclear engineers. For physics-based computational models, Verification,
Validation and Uncertainty Quantification (VVUQ) have been very widely
investigated and a lot of methodologies have been developed. However, VVUQ of
ML models has been relatively less studied, especially in nuclear engineering.
In this work, we focus on UQ of ML models as a preliminary step of ML VVUQ,
more specifically, Deep Neural Networks (DNNs) because they are the most widely
used supervised ML algorithm for both regression and classification tasks. This
work aims at quantifying the prediction, or approximation uncertainties of DNNs
when they are used as surrogate models for expensive physical models. Three
techniques for UQ of DNNs are compared, namely Monte Carlo Dropout (MCD), Deep
Ensembles (DE) and Bayesian Neural Networks (BNNs). Two nuclear engineering
examples are used to benchmark these methods, (1) time-dependent fission gas
release data using the Bison code, and (2) void fraction simulation based on
the BFBT benchmark using the TRACE code. It was found that the three methods
typically require different DNN architectures and hyperparameters to optimize
their performance. The UQ results also depend on the amount of training data
available and the nature of the data. Overall, all these three methods can
provide reasonable estimations of the approximation uncertainties. The
uncertainties are generally smaller when the mean predictions are close to the
test data, while the BNN methods usually produce larger uncertainties than MCD
and DE.
