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

Farah Alsafadi, Aidan Furlong, Xu Wu

TL;DR

The paper tackles data scarcity in critical heat flux (CHF) prediction by leveraging a conditional variational autoencoder (CVAE) to augment the NRC CHF dataset and comparing its performance to a fine-tuned deep neural network (DNN) baseline. It evaluates both models with uncertainty quantification (UQ) and domain-generalization analyses, using conditioning on five thermohydraulic inputs to generate or predict CHF values. Results show that the CVAE achieves slightly better error metrics and substantially tighter uncertainty than the DNN ensemble, and both models extrapolate reasonably to unseen conditions; the CVAE’s UQ is built-in via latent-space sampling, while the DNN requires multiple models for comparable reliability. The study demonstrates the viability of CVAEs for data augmentation in nuclear engineering and provides insights into model reliability across training and generalization domains, with potential extensions to transfer learning and diffusion-based generative methods.

Abstract

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.

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

TL;DR

The paper tackles data scarcity in critical heat flux (CHF) prediction by leveraging a conditional variational autoencoder (CVAE) to augment the NRC CHF dataset and comparing its performance to a fine-tuned deep neural network (DNN) baseline. It evaluates both models with uncertainty quantification (UQ) and domain-generalization analyses, using conditioning on five thermohydraulic inputs to generate or predict CHF values. Results show that the CVAE achieves slightly better error metrics and substantially tighter uncertainty than the DNN ensemble, and both models extrapolate reasonably to unseen conditions; the CVAE’s UQ is built-in via latent-space sampling, while the DNN requires multiple models for comparable reliability. The study demonstrates the viability of CVAEs for data augmentation in nuclear engineering and provides insights into model reliability across training and generalization domains, with potential extensions to transfer learning and diffusion-based generative methods.

Abstract

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.
Paper Structure (16 sections, 3 equations, 6 figures, 3 tables)

This paper contains 16 sections, 3 equations, 6 figures, 3 tables.

Table of Contents

  1. Introduction
  2. The CHF Experimental Dataset
  3. Methodologies
  4. DNNs
  5. VAEs and CVAEs
  6. The Generative and Predictive ML Models
  7. The CVAE Generative Model
  8. The DNN Predictive Model
  9. UQ of the ML Models
  10. Domain Generalization
  11. Results
  12. Results of CHF Generation and Prediction using CVAE and DNN
  13. Results of UQ
  14. Results of Domain Generalization Analysis
  15. Discussions
  16. ...and 1 more sections

Figures (6)

  • Figure 1: The distributions and correlations of the TH parameters and CHF values in the NRC CHF dataset.
  • Figure 2: Illustration of the structure of a CVAE generative model.
  • Figure 3: Performance comparison of the DNN and CVAE models.
  • Figure 4: Comparison of the CHF-TH-parameter pairwise correlations between the real data and the CVAE generated data.
  • Figure 5: Comparison of the CHF-TH-parameter pairwise correlations between the real data and the DNN predicted data.
  • ...and 1 more figures