# Uncertainty Quantification for Data-Driven Machine Learning Models in Nuclear Engineering Applications: Where We Are and What Do We Need?

arXiv: https://arxiv.org/abs/2503.17385 · HTML: https://mlsanity.com/paper/2503.17385/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 68 references that are in the map.
- First posted on arXiv 16 Mar 2025.

## Builds on (most cited first, 18 of 18)

- [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)
- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Generalizing to Unseen Domains: A Survey on Domain Generalization](https://mlsanity.com/paper/2103.03097/) (2021)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons](https://mlsanity.com/paper/2201.07766/) (2022)
- [Bayesian Neural Networks: An Introduction and Survey](https://mlsanity.com/paper/2006.12024/) (2020)
- [Quantification of Deep Neural Network Prediction Uncertainties for VVUQ of Machine Learning Models](https://mlsanity.com/paper/2206.14615/) (2022)
- [Prediction and Uncertainty Quantification of SAFARI-1 Axial Neutron Flux Profiles with Neural Networks](https://mlsanity.com/paper/2211.08654/) (2022)
- [Predicting Critical Heat Flux with Uncertainty Quantification and Domain Generalization Using Conditional Variational Autoencoders and Deep Neural Networks](https://mlsanity.com/paper/2409.05790/) (2024)
- [The ICSCREAM methodology: Identification of penalizing configurations in computer experiments using screening and metamodel -- Applications in thermal-hydraulics](https://mlsanity.com/paper/2004.04663/) (2020)
- [Functional PCA and Deep Neural Networks-based Bayesian Inverse Uncertainty Quantification with Transient Experimental Data](https://mlsanity.com/paper/2307.05592/) (2023)
- [Multi-output Gaussian processes for inverse uncertainty quantification in neutron noise analysis](https://mlsanity.com/paper/2211.02465/) (2022)
- [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)
- [Data-Driven Prediction and Uncertainty Quantification of PWR Crud-Induced Power Shift Using Convolutional Neural Networks](https://mlsanity.com/paper/2407.04726/) (2024)

## Built on by (most cited first, 2 of 2)

- [Quantifying Out-of-Training Uncertainty of Neural-Network based Turbulence Closures](https://mlsanity.com/paper/2508.16891/) (2025)
- [A Three-Stage Bayesian Transfer Learning Framework to Improve Predictions in Data-Scarce Domains](https://mlsanity.com/paper/2510.26541/) (2025)

## Abstract (arXiv)

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.