# Quantification of Deep Neural Network Prediction Uncertainties for VVUQ of Machine Learning Models

arXiv: https://arxiv.org/abs/2206.14615 · HTML: https://mlsanity.com/paper/2206.14615/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 44 references that are in the map.
- First posted on arXiv 27 Jun 2022.

## Builds on (most cited first, 11 of 11)

- [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)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (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 Tutorial on Principal Component Analysis](https://mlsanity.com/paper/1404.1100/) (2014)
- [Bayesian Neural Networks: An Introduction and Survey](https://mlsanity.com/paper/2006.12024/) (2020)
- [Development and Assessment of a Nearly Autonomous Management and Control System for Advanced Reactors](https://mlsanity.com/paper/2008.12888/) (2020)
- [From Physics-Based Models to Predictive Digital Twins via Interpretable Machine Learning](https://mlsanity.com/paper/2004.11356/) (2020)
- [Deep Learning Interfacial Momentum Closures in Coarse-Mesh CFD Two-Phase Flow Simulation Using Validation Data](https://mlsanity.com/paper/2005.03767/) (2020)
- [Digital-Twin-Based Improvements to Diagnosis, Prognosis, Strategy Assessment, and Discrepancy Checking in a Nearly Autonomous Management and Control System](https://mlsanity.com/paper/2105.11039/) (2021)

## Built on by (most cited first, 9 of 9)

- [A Framework for Strategic Discovery of Credible Neural Network Surrogate Models under Uncertainty](https://mlsanity.com/paper/2403.08901/) (2024)
- [Fast and Accurate Reduced-Order Modeling of a MOOSE-based Additive Manufacturing Model with Operator Learning](https://mlsanity.com/paper/2308.02462/) (2023)
- [Functional PCA and Deep Neural Networks-based Bayesian Inverse Uncertainty Quantification with Transient Experimental Data](https://mlsanity.com/paper/2307.05592/) (2023)
- [Physics-Based Hybrid Machine Learning for Critical Heat Flux Prediction with Uncertainty Quantification](https://mlsanity.com/paper/2502.19357/) (2025)
- [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)
- [Don't Collapse Your Features: Why CenterLoss Hurts OOD Detection and Multi-Scale Mahalanobis Wins](https://mlsanity.com/paper/2605.21493/) (2026)
- [Evidence-Guided Neural Architecture Selection under Uncertainty for Subject-Specific Blood Glucose Forecasting](https://mlsanity.com/paper/2606.05373/) (2026)

## Abstract (arXiv)

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.