# Clustering and Uncertainty Analysis to Improve the Machine Learning-based Predictions of SAFARI-1 Control Follower Assembly Axial Neutron Flux Profiles

arXiv: https://arxiv.org/abs/2312.14193 · HTML: https://mlsanity.com/paper/2312.14193/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 43 references that are in the map.
- First posted on arXiv 20 Dec 2023.

## Builds on (most cited first, 9 of 9)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons](https://mlsanity.com/paper/2201.07766/) (2022)
- [A Review of Deep Learning with Special Emphasis on Architectures, Applications and Recent Trends](https://mlsanity.com/paper/1905.13294/) (2019)
- [Survey of state-of-the-art mixed data clustering algorithms](https://mlsanity.com/paper/1811.04364/) (2018)
- [Quantification of Deep Neural Network Prediction Uncertainties for VVUQ of Machine Learning Models](https://mlsanity.com/paper/2206.14615/) (2022)
- [Data-driven modeling for boiling heat transfer: using deep neural networks and high-fidelity simulation results](https://mlsanity.com/paper/1808.01859/) (2018)
- [Prediction and Uncertainty Quantification of SAFARI-1 Axial Neutron Flux Profiles with Neural Networks](https://mlsanity.com/paper/2211.08654/) (2022)

## Built on by (most cited first, 1 of 1)

- [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)

## Abstract (arXiv)

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.