Generative

Deep Generative Modeling

The confluence of ultrafast computers with large memory, rapid progress in AI/ML algorithms, and the ready availability of large datasets place multiple engineering fields at the threshold of dramatic progress. However, a unique challenge in NE is data scarcity because experimentation on nuclear systems is usually more expensive and time-consuming than most other disciplines. Particularly concerning is the lack of data for advanced reactor design and safety analysis, raising challenges for utilizing ML in licensing analyses of advanced nuclear reactors. In these cases, we need to move beyond “throw more data and re-train” at the problem, which is the common solution in areas such as computer vision and natural language processing that have access to “big data”. To this end, we are developing innovative data augmentation methods by leveraging deep generative learning and developing new techniques for nuclear-specific applications. Deep generative learning is an unsupervised ML technique that aims at discovering and learning the regularities or patterns in existing data in order to generate new samples that plausibly could have been drawn from the real dataset. In fact, a successful generative model may be able to generate new data that are indistinguishable from the real data. DNNs are usually used as the build blocks for deep generative learning models, where they are trained to approximate the sophisticated probability distributions underlying the real data. The general idea is to estimate and maximize the likelihood of the real data and create new synthetic data from the learned underlying distributions. In this way, the dataset can be significantly expanded, enabling us to train more accurate SciML models for other tasks and reduce over-fitting which is common when the dataset is limited.

We have investigated the effectiveness of various DGMs for overcoming data scarcity in nuclear energy applications, including generative adversarial networks (GANs), normalizing flows (NFs), variational autoencoders (VAEs), conditional VAEs (CVAEs) and diffusion models (DMs). In our recent works, 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 performance of the conditional DM was also assessed through direct comparison with true CHF values using multiple error metrics. 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.

Relevant publications:

1. Alsafadi, F., Akins, A., and Wu, X. (2026). Development of physics-consistent conditional diffusion model to overcome data scarcity in critical heat flux. Energy and AI, 24:100702.
   https://doi.org/10.1016/j.egyai.2026.100702
2. Alsafadi, F., Yaseen, M., and Wu, X. (2025). An Investigation on Machine Learning Predictive Accuracy Improvement and Uncertainty Reduction using VAE-based Data Augmentation. Nuclear Engineering and Design, 445:114433.
   https://doi.org/10.1016/j.nucengdes.2025.114433
3. Furlong, A., Zhao, X., Salko, R., and Wu, X. (2025). Physics-based hybrid machine learning for critical heat flux prediction with uncertainty quantification. Applied Thermal Engineering, 279:127447.
   https://doi.org/10.1016/j.applthermaleng.2025.127447
4. Alsafadi, F., Furlong, A., and Wu, X. (2025). Predicting critical heat flux with uncertainty quantification and domain generalization using conditional variational autoencoders and deep neural networks. Annals of Nuclear Energy, 220:111502.
   https://doi.org/10.1016/j.anucene.2025.111502
5. Alsafadi, F. and Wu, X. (2023). Deep Generative Modeling-based Data Augmentation with Demonstration using the BFBT Benchmark Void Fraction Datasets. Nuclear Engineering and Design, 415:112712
   https://www.sciencedirect.com/science/article/pii/S0029549323005617

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