Deep generative modeling provides a powerful pathway to overcome data scarcity in energy-related applications where experimental data are often limited, costly, or difficult to obtain. By learning the underlying probability distribution of the training dataset, deep generative models, such as the diffusion model (DM), can generate high-fidelity synthetic samples that statistically resemble the training data. Such synthetic data generation can significantly enrich the size and diversity of the available training data, and more importantly, improve the robustness of downstream machine learning models in predictive tasks. The objective of this paper is to investigate the effectiveness of DM for overcoming data scarcity in nuclear energy applications. By leveraging a public dataset on critical heat flux (CHF) that cover a wide range of commercial nuclear reactor operational conditions, we developed a DM that can generate an arbitrary amount of synthetic samples for augmenting of the CHF dataset. Since a vanilla DM can only generate samples randomly, we also developed a conditional DM capable of generating targeted CHF data under user-specified thermal-hydraulic conditions. The performance of the DM was evaluated based on their ability to capture empirical feature distributions and pair-wise correlations, as well as to maintain physical consistency. The results showed that both the DM and conditional DM can successfully generate realistic and physics-consistent CHF data. Furthermore, uncertainty quantification was performed to establish confidence in the generated data. The results demonstrated that the conditional DM is highly effective in augmenting CHF data while maintaining acceptable levels of uncertainty.

Deep generative models (DGMs) have proven to be powerful in generating realistic data samples. Their capability to learn the underlying distribution of a dataset enable them to generate synthetic data samples that closely resemble the original training dataset, thus addressing the challenge of data scarcity. In this work, we investigated the capabilities of DGMs by developing a conditional variational autoencoder (CVAE) model to augment the critical heat flux (CHF) measurement data that was used to generate the 2006 Groeneveld lookup table. To determine how this approach compared to traditional methods, a fine-tuned deep neural network (DNN) regression model was created and evaluated with the same dataset. Both the CVAE and DNN models achieved small mean absolute relative errors, with the CVAE model maintaining more favorable results. To quantify the uncertainty in the model's predictions, uncertainty quantification (UQ) was performed with repeated sampling of the CVAE model and ensembling of the DNN model. Following UQ, the DNN ensemble notably improved performance when compared to the baseline DNN model, while the CVAE model achieved similar results to its non-UQ results. The CVAE model was shown to have significantly less variability and a higher confidence after assessment of the prediction-wise relative standard deviations. Evaluating domain generalization, both models achieved small mean error values when predicting both inside and outside the training domain, with predictions outside the training domain showing slightly larger errors. Overall, the CVAE model was comparable to the DNN regression model in predicting CHF values but with better uncertainty behavior.