# Prediction and Uncertainty Quantification of SAFARI-1 Axial Neutron Flux Profiles with Neural Networks

arXiv: https://arxiv.org/abs/2211.08654 · HTML: https://mlsanity.com/paper/2211.08654/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 47 references that are in the map.
- First posted on arXiv 16 Nov 2022.

## Builds on (most cited first, 5 of 5)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Bayesian Neural Networks: An Introduction and Survey](https://mlsanity.com/paper/2006.12024/) (2020)
- [A Review of Deep Learning with Special Emphasis on Architectures, Applications and Recent Trends](https://mlsanity.com/paper/1905.13294/) (2019)
- [Data-driven modeling for boiling heat transfer: using deep neural networks and high-fidelity simulation results](https://mlsanity.com/paper/1808.01859/) (2018)

## Built on by (most cited first, 6 of 6)

- [Deep Neural Operator Driven Real Time Inference for Nuclear Systems to Enable Digital Twin Solutions](https://mlsanity.com/paper/2308.07523/) (2023)
- [Functional PCA and Deep Neural Networks-based Bayesian Inverse Uncertainty Quantification with Transient Experimental Data](https://mlsanity.com/paper/2307.05592/) (2023)
- [Uncertainty Quantification for Data-Driven Machine Learning Models in Nuclear Engineering Applications: Where We Are and What Do We Need?](https://mlsanity.com/paper/2503.17385/) (2025)
- [Clustering and Uncertainty Analysis to Improve the Machine Learning-based Predictions of SAFARI-1 Control Follower Assembly Axial Neutron Flux Profiles](https://mlsanity.com/paper/2312.14193/) (2023)
- [An Investigation on Machine Learning Predictive Accuracy Improvement and Uncertainty Reduction using VAE-based Data Augmentation](https://mlsanity.com/paper/2410.19063/) (2024)
- [PTNO: Training Neural Operators with Noisy Monte Carlo Estimates for Particle Transport Problems](https://mlsanity.com/paper/2609.40090/) (2026)

## Abstract (arXiv)

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).