# Predicting Critical Heat Flux with Uncertainty Quantification and Domain Generalization Using Conditional Variational Autoencoders and Deep Neural Networks

arXiv: https://arxiv.org/abs/2409.05790 · HTML: https://mlsanity.com/paper/2409.05790/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 35 references that are in the map.
- First posted on arXiv 9 Sep 2024.

## Builds on (most cited first, 13 of 13)

- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems](https://mlsanity.com/paper/1603.04467/) (2016)
- [Tune: A Research Platform for Distributed Model Selection and Training](https://mlsanity.com/paper/1807.05118/) (2018)
- [An Introduction to Deep Generative Modeling](https://mlsanity.com/paper/2103.05180/) (2021)
- [An Uncertain Future: Forecasting from Static Images using Variational Autoencoders](https://mlsanity.com/paper/1606.07873/) (2016)
- [Amortised MAP Inference for Image Super-resolution](https://mlsanity.com/paper/1610.04490/) (2016)
- [Semi Conditional Variational Auto-Encoder for Flow Reconstruction and Uncertainty Quantification from Limited Observations](https://mlsanity.com/paper/2007.09644/) (2020)
- [Dizygotic Conditional Variational AutoEncoder for Multi-Modal and Partial Modality Absent Few-Shot Learning](https://mlsanity.com/paper/2106.14467/) (2021)
- [Deep Generative Modeling-based Data Augmentation with Demonstration using the BFBT Benchmark Void Fraction Datasets](https://mlsanity.com/paper/2308.10120/) (2023)

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

- [Bayesian optimized deep ensemble for uncertainty quantification of deep neural networks: a system safety case study on sodium fast reactor thermal stratification modeling](https://mlsanity.com/paper/2412.08776/) (2024)
- [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)
- [An Investigation on Machine Learning Predictive Accuracy Improvement and Uncertainty Reduction using VAE-based Data Augmentation](https://mlsanity.com/paper/2410.19063/) (2024)
- [A Three-Stage Bayesian Transfer Learning Framework to Improve Predictions in Data-Scarce Domains](https://mlsanity.com/paper/2510.26541/) (2025)
- [Towards Overcoming Data Scarcity in Nuclear Energy: A Study on Critical Heat Flux with Physics-consistent Conditional Diffusion Model](https://mlsanity.com/paper/2511.16207/) (2025)

## Abstract (arXiv)

Deep generative models (DGMs) can generate synthetic data samples that closely resemble the original dataset, addressing data scarcity. In this work, we developed a conditional variational autoencoder (CVAE) to augment critical heat flux (CHF) data used for the 2006 Groeneveld lookup table. To compare with traditional methods, a fine-tuned deep neural network (DNN) regression model was evaluated on the same dataset. Both models achieved small mean absolute relative errors, with the CVAE showing more favorable results. Uncertainty quantification (UQ) was performed using repeated CVAE sampling and DNN ensembling. The DNN ensemble improved performance over the baseline, while the CVAE maintained consistent results with less variability and higher confidence. Both models achieved small errors inside and outside the training domain, with slightly larger errors outside. Overall, the CVAE performed better than the DNN in predicting CHF and exhibited better uncertainty behavior.